KYIV, Ukraine—In a surprise visit to Kyiv on Sunday, Polish President Andrzej Duda said that only Ukraine should decide any terms upon which it pursues peace with Moscow, and called for a complete removal of all Russian troops in Ukraine, breaking with European leaders who have suggested the partly-occupied country should accede to some of its attacker’s demands.

Mr. Duda, the first foreign leader to address Ukraine’s parliament in person since Russia’s Feb. 24 invasion, also called for the European Union to increase sanctions on Russia and accept Ukraine as its newest member.

In a speech interrupted repeatedly by standing applause, with Polish flags displayed across Kyiv’s unicameral parliament, Mr. Duda said that Poland supported Ukraine’s right to make its own choices in any discussions with Russia.

“There are disturbing voices appearing within Europe demanding that Ukraine should acknowledge the demands of Russia. I want to say clearly that only Ukraine has the right to decide about itself,” he said. “Nothing should be decided about you, without you.”

His comments come after some European leaders have proposed offering Russia enough concessions to allow President Vladimir Putin to save face and end the war. Italy said Friday it had presented a four-point peace plan to United Nations Secretary-General António Guterres. The proposal would declare Ukraine a neutral country, grant autonomy to Ukraine’s Crimea and Donbas, and wind down the sanctions on Russia, according to a report in Italian newspaper La Repubblica, whose points mostly mirrored comments made publicly by Prime Minister Mario Draghi and other Western European leaders.

Mr. Duda didn’t name which countries were pressing Ukraine to accept Russia’s demands. On Saturday, former Italian Prime Minister Silvio Berlusconi called for Europe to “make a peace proposal to get the Ukrainians to accept Putin’s demands,” comments carried on Polish state television.

“The world and the international community should demand an end to Russia’s aggression and a complete withdrawal from the territory of Ukraine,” Mr. Duda said. “If for the sake of a bit of peace of economic interest or political ambition even a centimeter of Ukrainian soil and a piece of their sovereignty will be sacrificed, then this will be a huge blow not only for Ukraine, but also for the Western community.”

He also called for the EU to go further in its efforts to cut itself off from the Russian economy. The bloc is close to approving a new package of sanctions that would include an embargo on Russian crude oil, though Hungary’s Prime Minister Viktor Orban is standing in the way.

“I will not rest until Ukraine is a member of the European Union,” Mr. Duda said.

President Volodymyr Zelensky, who also spoke before parliament, said that his country would introduce a special legal status for Poles residing in Ukraine, a reciprocal offer for Poland, which has taken in several million Ukrainians since the war began. An official in Mr. Duda’s office said the two governments were interested in pursuing an agreement similar to the 1963 Élysée Treaty, in which France and West Germany agreed to meet regularly and coordinate their major policy decisions, a treaty that became a basis for closer European integration after World War II.

Mr. Duda’s visit to Kyiv was his second since the war began. Mr. Duda—who told The Wall Street Journal in an interview this month that he speaks by phone nearly every day to Mr. Zelensky—is currently looking to help Ukraine move its grain to international markets, circumventing Russia’s naval chokehold in the Black Sea. Next month, Mr. Duda is traveling to Egypt, the world’s largest wheat importer, to help coordinate those shipments.

Mr. Duda met with Mr. Zelensky to discuss how to get Ukraine’s grain harvest out of the country via ports and rail lines in Poland and its neighbors.

Poland's President Andrzej Duda and Ukrainian President Volodymyr Zelensky in the capital of Kyiv on Sunday

Photo: JAKUB SZYMCZUK/POLISH PRESIDENCY/REUTERS

Warehouses in Ukraine are filled with wheat and other grain that the country, one of the world’s largest exporters, has been unable to ship since February. Ukraine also relies on shipments from and through Poland to alleviate the crippling fuel shortage that was caused by Russia striking Ukraine’s oil refineries and fuel-storage facilities.

Ukrainian leaders say the country needs a massive increase in weapons supplies to continue resisting Russia, to liberate occupied territories and to try to unblock shipping lanes.

President Biden on Saturday signed a $40 billion bill that includes an additional $6 billion in direct military aid and $8.8 billion in economic assistance to Ukraine. The Biden administration hasn’t specified what weapons it plans to supply with these new funds, and hasn’t indicated whether it will accept Ukrainian requests for long-range artillery and missile systems such as the Himars multiple-launch rocket system that Kyiv says it needs most urgently.

A grain warehouse damaged during fighting in the Kharkiv region.

Photo: John Moore/Getty Images

A cemetery on the southern outskirts of the city of Kharkiv.

Photo: dimitar dilkoff/Agence France-Presse/Getty Images

Ukrainian resistance forced Mr. Putin in late March to abandon plans to seize Kyiv, precipitating a Russian withdrawal from northern Ukraine. In this new phase of the war, Russia’s declared objective was to capture the entirety of the eastern Donetsk and Luhansk regions, collectively known as Donbas. Mr. Putin in February recognized the independence of the Russian-controlled statelets, known as the Donetsk and Luhansk people’s republics, and no longer considers Donbas part of Ukraine.

In addition to about three-quarters of Donbas, Russia currently controls parts of the Kharkiv region, where its forces are retreating under Ukrainian counterattacks, and a swath of southern Ukraine’s Kherson and Zaporizhzhia regions. Signs of Ukrainian resistance are growing in these occupied areas, where Russia has replaced local administrations with collaborators and is introducing its ruble as the currency instead of the Ukrainian hryvnia.

In Enerhodar, a city in the Zaporizhzhia region that is home to Europe’s largest nuclear power plant, unknown assailants Sunday placed an explosive device at the residence of the Russian-appointed mayor, Andriy Shevchyk, according to Russian and Ukrainian reports. Enerhodar’s legitimately elected mayor, Dmytro Orlov, said in a social-media post that Mr. Shevchyk and his bodyguards were injured and hospitalized.

Residents of Severodonetsk have seen their city become a focal point for Russia’s offensive in eastern Ukraine.

Photo: yasuyoshi chiba/Agence France-Presse/Getty Images

The ruins of an apartment block in Kharkiv.

Photo: John Moore/Getty Images

Russia’s broader effort to capture the entirety of Donbas has stalled after more than a month of fighting. Moscow’s current offensive focuses on a much narrower salient that includes Severodonetsk, the administrative center of Ukrainian-controlled Luhansk region, and nearby towns. Russia’s Defense Minister Sergei Shoigu said Saturday that Russia is close to completing the “liberation” of the Luhansk region.

Russia’s initial effort to cut the only road connecting Severodonetsk to the rest of government-controlled Donbas failed two weeks ago, after Ukrainian forces destroyed Russian pontoon bridging attempts. Russia lost some 90 tanks and other armored vehicles in that attempt, according to drone footage, and has acknowledged the death of its 12th Engineers Brigade commander, among other casualties.

Russian forces were more successful in recent days as they moved toward the road from the south, developing an offensive from the town of Popasna, which Moscow seized early this month. On Saturday, a Russian Tulpan self-propelled heavy mortar destroyed the main bridge connecting Severodonetsk to government-controlled areas, making the defense of the embattled city even more difficult.

Russian TV filmed the Tulpan, a relatively rare vehicle, firing 220 mm rounds from the town of Rubizhne near Severodonetsk. Ukrainian forces geolocated the position from the footage and destroyed the vehicle hours later, said Ukraine’s Luhansk administration chief, Serhiy Haidai. Open-source intelligence analysts located drone footage of the strike on the Tulpan to within 200 meters of the footage broadcast on Russian TV.

The rubble of a collapsed tram depot in Mariupol, where Russia’s forces have taken full control of the city after months of fighting.

Photo: alessandro guerra/Shutterstock

Russia said it had taken complete control of the southeastern port city of Mariupol on Saturday after the surrender of the last remaining Ukrainian forces there. Mr. Zelensky described the soldiers and marines who had defended Mariupol through a monthslong siege as national heroes. He said the military had told them to get out and save their lives.

Russia’s Defense Ministry said a final group of 531 Ukrainian fighters had been evacuated from bunkers under the sprawling Azovstal steel plant to Russian-controlled territory, bringing the total number of prisoners taken from the plant to 2,439.

“The underground facilities of the enterprise, where the militants were hiding, came under the full control of the Russian armed forces,” the ministry said.

By holding out for weeks in ever-smaller pockets, Ukrainian defenders tied up large numbers of Russian troops, preventing their deployment elsewhere.

—Laurence Norman and Natalia Ojewska contributed to this article.

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com and Drew Hinshaw at drew.hinshaw@wsj.com