Ukraine and Russia said they made some progress in talks to end the war, with Kyiv presenting its proposal for a neutral status and international security guarantees as Moscow continued deadly strikes across Ukraine despite promises to focus its campaign on the eastern Donbas region.

Though the latest round of negotiations, opened by Turkish President Recep Tayyip Erdogan in Istanbul, made advances toward drafting a peace treaty, violence continued unabated, with dozens of reported civilian casualties.

In a sign of progress, Russian President Vladimir Putin agreed to meet Ukrainian President Volodymyr Zelensky for the initialing of the treaty once the negotiations are completed, said Moscow’s chief negotiator, Vladimir Medinsky. He also said that, in a show of good will, Russia would limit its operations near Kyiv and the northern Ukrainian city of Chernihiv, though that step didn’t amount to a cease-fire.

As the talks began, a Russian cruise missile hit the regional government building in the southern city of Mykolaiv during normal work hours. Rescuers were searching the damaged building, half of which was destroyed, for survivors. Ukraine’s state emergency service put the initial death toll at 12 people, with 33 others injured. Mykolaiv Gov. Vitaliy Kim said that Russia waited for the building to be full of employees before the strike. He added that he wasn’t hurt because he overslept on Tuesday.

Another Russian missile strike on Tuesday destroyed the fuel depot in the western Ukrainian town of Starokostyantyniv, the local mayor said.

U.S. Secretary of State Antony Blinken, who wasn’t part of the talks in Turkey, said he had seen no evidence that Moscow is committed to meaningful peace negotiations.

“There is what Russia says and what Russia does,” Mr. Blinken said Tuesday in Rabat, Morocco. “And we’re focused on the latter.”

Russian Defense Minister Sergei Shoigu said Tuesday that Moscow has switched its strategy in Ukraine and would now focus on the parts of the Donetsk and Luhansk regions that remain under Kyiv’s control. Mr. Putin last month recognized the so-called Donetsk and Luhansk people’s republics as independent nations in their claimed borders, which included the two-thirds of the region administered by Kyiv at the time.

“In general, the main objectives of the first stage of the operation have been achieved,” Mr. Shoigu said. “The combat capacity of Ukrainian armed forces has been significantly lowered, which allows us to focus our main attention and efforts on the principal goal—liberating Donbas.”

Russia’s initial plan for the war was to quickly seize the capital, Kyiv, and other big cities, installing a puppet regime. Mr. Putin at the time publicly called on Ukrainian forces to stage a coup and oust Mr. Zelensky. Fierce Ukrainian resistance has inflicted heavy losses on Russian forces since then.

A car marked with the Russian word for “children” at an evacuation point in Zaporizhzhia, in southeastern Ukraine, on Tuesday.

Photo: emre caylak/Agence France-Presse/Getty Images

Mourners gathered on Monday for the funeral of a Ukrainian serviceman killed in action in Irpin, near Kyiv.

Photo: Christopher Occhicone for the Wall Street Journal

In Donbas, Russian troops have entered the port city of Mariupol, besieged for about a month, but fierce battles with Ukrainian forces continue. Local officials have put the civilian death toll in the city, where many neighborhoods have been leveled, at over 5,000. In the rest of Donbas, Russia so far has failed to seize the principal cities of Kramatorsk, Slovyansk and Severodonetsk.

Ukrainian troops have launched counteroffensives in several areas in recent weeks, including near Kyiv and Chernihiv, and in the regions of Mykolaiv, Kharkiv and Sumy. On Tuesday, Ukraine’s military said it destroyed two battalion tactical groups of the Russian army’s 200th infantry brigade near Kharkiv and killed the brigade’s commander, Col. Denis Kurilo. There was no immediate confirmation of the claim by Russia.

Ukrainian officials reported advances in other parts of the country.

Oleksandr Vilkul, mayor of Kryvyi Rih in central Ukraine, said Ukrainian forces had repelled Russian attacks and pushed Russian forces 25 miles from the city, which is Mr. Zelensky’s hometown.

“The main thing is that after the stress of the first days, we have realized that we can not only halt the enemy, but strike and defeat it,” Mr. Vilkul said in a video address.

While Ukrainian officials were cautious about Russian promises of de-escalation near Kyiv and Chernihiv, they welcomed the step, saying that it could facilitate humanitarian relief efforts. Chernihiv has been under siege for weeks, and its mayor Tuesday said at least 350 civilians had been killed in the city.

The Ukrainian proposal in Istanbul calls for binding guarantees for Ukraine’s security from the U.S., U.K., France, Turkey, Germany, Canada, Poland and Israel.

“This is the system we would like to build the future of Ukraine on,” said Ukrainian negotiator David Arakhamia, the majority leader in the country’s parliament.

“We want an international mechanism of security guarantees where guarantor countries will act in a similar way to NATO’s article number five,” Mr. Arakhamia said, referring to the North Atlantic Treaty Organization’s mutual-defense promise.

A man inside the regional government building in Mykolaiv, Ukraine, that was hit in a Russian attack.

Photo: Diana Zeyneb Alhindawi for The Wall Street Journal

Fire damage at a school in the Kyiv-area village of Rudnyts’ke.

Photo: Andrea Filigheddu/Zuma Press

Ukrainian presidential adviser Mykhailo Podolyak said that the arrangement would be subject to a referendum of the Ukrainian people, as well as the approval of the guarantor countries and their parliaments. Mr. Zelensky has said that any referendum can only be held following a full Russian withdrawal to the contact line in Donbas before Feb. 24.

Mr. Podolyak said that Ukraine had offered Russia a 15-year period of negotiations on the status of Crimea, which Russia annexed by force in 2014, and that the status of the areas of Donbas controlled by Russia before Feb. 24 would be discussed directly by Mr. Putin and Mr. Zelensky.

Russia’s Mr. Medinsky confirmed the receipt of written proposals from the Ukrainian side, saying they would be communicated to Moscow.

Turkey’s Mr. Erdogan briefly visited the Russian and Ukrainian negotiators, who met in a former Ottoman palace on the banks of the Bosporus.

“We are entering a period when concrete results should be achieved from negotiations,” Mr. Erdogan said. “The whole world is waiting for good news from you.”

Russian oligarch Roman Abramovich, who survived an alleged poisoning earlier this month, was photographed inside the room with the negotiators. Mr. Abramovich appeared to be greeting Mr. Erdogan and sitting at a table with Russian and Ukrainian officials, according to news footage reviewed by The Wall Street Journal.

Before the talks, Mr. Zelensky escalated his criticism of Western leaders for their reluctance to tighten sanctions on Russia or provide heavier weapons for Ukraine’s defense.

Turkish President Recep Tayyip Erdogan, wearing a red tie, greeted negotiators Tuesday before the Russia-Ukraine talks in Istanbul.

Photo: MURAT CETINMUHURDAR/PPO/via REUTERS

Russian oligarch Roman Abramovich, wearing a blue suit, listened through headphones as Turkey’s president addressed negotiators.

Photo: TURKISH PRESIDENCY/via REUTERS

In a televised address late Monday, Mr. Zelensky called for tougher sanctions, including an embargo on Russian oil sales to the European Union, to be implemented immediately rather than waiting for Moscow to step up its attacks, for example by using chemical weapons.

“If the sanctions packages are weak or don’t work well enough, if they can be circumvented, it creates a dangerous illusion for the Russians that they can afford to continue what they are doing now,” said the Ukrainian president. “And Ukrainians pay for this with their lives. Thousands of lives.”

Ties between Russia and EU countries have deteriorated sharply following Mr. Putin’s decision to invade Ukraine. On Tuesday, four European countries announced they were kicking out more than 40 Russian officials over national security threats, citing spying and influence operations as reasons. Russia also announced Tuesday it was expelling a number of diplomats from the EU’s Baltic countries.

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But the EU has so far rejected calls to sever its main business dealings with Russia: the purchase of oil and gas, which are Moscow’s main sources of export earnings. The U.S. banned Russian oil, gas and coal imports on March 8.

Many observers believe public pressure on EU leaders to act could become overwhelming if Mr. Putin orders the use of chemical or other unconventional weapons in Ukraine. At an EU summit last week, some officials argued that the bloc should impose further sanctions only in reaction to a further escalation by Russia.

“There are simply no words. Just think about what it has come down to. Waiting for chemical weapons. We, living people, have to wait,” Mr. Zelensky said in his televised address. “Doesn’t everything the Russian military has done so far deserve an oil embargo?”

Destroyed Russian military equipment on a road near the northern city of Chernihiv, Ukraine, on Monday.

Photo: andrzej lange/Shutterstock

People fleeing the fighting in Ukraine waited to receive aid on the outskirts of Kyiv on Tuesday.

Photo: Rodrigo Abd/Associated Press

Some eastern and northern EU countries support sanctions on Russian energy imports, but Germany, Europe’s biggest economy, has rejected an immediate cutoff of Russian oil and gas. German Chancellor Olaf Scholz on Sunday warned of devastating economic consequences for his country if it bans Russian oil, dismissing studies by economists that say the impact would be manageable.

German officials have, however, said the country would find ways to cope if Moscow, rather than Berlin, cuts off oil and gas deliveries, raising doubts about Mr. Scholz’s claim that Germany couldn’t cope without Russian energy imports.

Losing access to Russian gas during colder months would mean activating German emergency plans to conserve fuel for heating, including suspending some industrial activities—such as in the chemicals sector—that use gas in the production process.

Some German politicians, such as former Finance Minister Wolfgang Schäuble, have called for an immediate if temporary embargo on all energy purchases from Russia to destroy the economic underpinnings of Mr. Putin’s military offensive.

Mr. Zelensky also called for more weapons, including warplanes, tanks, artillery and shells.

“Ukrainians should not die just because someone cannot find enough courage to hand over weapons to Ukraine,” he said. “Fear always makes you an accomplice.”

—Yuliya Chernova, Marcus Walker, Elvan Kivilcim, Bojan Pancevski, Courtney McBride and Laurence Norman contributed to this article.

Write to James Marson at james.marson@wsj.com, Yaroslav Trofimov at yaroslav.trofimov@wsj.com and Jared Malsin at jared.malsin@wsj.com