Small bands of Russian soldiers thrust deeper into eastern Ukraine on Tuesday before a summit between Russian President Vladimir Putin and U.S. President Donald Trump, which European leaders fear could end in peace terms imposed on an unlawfully shrunken Ukraine.

In one of the most extensive incursions so far this year, Russian troops advanced near the coal-mining town of Dobropillia, part of Putin's campaign to take full control of Ukraine's Donetsk region. Ukraine's military dispatched reserve troops, saying they were in difficult combat against Russian soldiers.

Trump has said any peace deal would involve "some swapping of territories to the betterment of both" Russia and Ukraine, which has up to now depended on the United States as its main arms supplier.

But because all of the areas being contested lie within Ukraine, Ukrainian President Volodymyr Zelenskyy and his European Union allies fear he'll face pressure to give up far more than Russia does.

Trump's administration tempered expectations on Tuesday for major progress toward a ceasefire, calling his pending Friday meeting with Putin in Alaska a "listening exercise."

Along that line, U.S. Secretary of State Marco Rubio said the president wanted to size up Putin directly.

"The president feels like, 'Look, I've got to look at this guy across the table. I need to see him face to face. I need to hear him one on one. I need to make an assessment by looking at him,'" Rubio told WABC radio in New York on Tuesday.

Zelenskyy and most of his European counterparts have said a lasting peace cannot be secured without Ukraine at the negotiating table and that a deal must comply with international law, Ukraine's sovereignty and its territorial integrity. They will hold a virtual meeting with Trump on Wednesday to underscore those concerns.

"Substantive and productive talks about us without us will not work," Zelenskyy said in an interview on Tuesday with NewsNation. "They are possible, but they will not be accepted in practice. Just as I cannot say anything about another state or make decisions for it."

The Ukrainian leader said Russia must agree to a ceasefire before territorial issues are discussed. He would reject any Russian proposal that Ukraine pull its troops from the eastern Donbas region and cede its defensive lines.

Trump seeks 'better understanding'

Asked why Zelenskyy wasn't joining the Alaska summit, a White House spokesperson said Tuesday that the bilateral meeting had been proposed by Putin and that Trump accepted to get a "better understanding" of how to end the war.

"This is for the president to go and to get a more firm and better understanding of how we can hopefully bring this war to an end," press secretary Karoline Leavitt told reporters.

Trump is open to a trilateral meeting with Putin and Zelenskyy later, Leavitt said.

WATCH | Trump, Putin to meet in Alaska:

Trump, Putin set to meet in Alaska for further ceasefire negotiations | Hanomansing Tonight

U.S. President Donald Trump and Russian President Vladimir Putin are set to meet in Alaska for the first U.S.-Russia summit since 2021. It comes after a ceasefire deadline for Putin to agree to a Ukraine ceasefire passed without an announcement on Friday.

Ukraine faces a troop shortage, easing the path for the latest Russian advances.

Ukraine's military, meanwhile, said it had retaken two villages in the eastern region of Sumy on Monday, part of a small reversal in more than a year of slow, attritional Russian gains in the southeast.

Russia, which launched its full-scale invasion of Ukraine in February 2022, has mounted a new offensive this year in Sumy after Putin demanded a "buffer zone" there.

Ukraine and its European allies fear that Trump, keen to claim credit for making peace and seal new business deals with Russia's government, will end up rewarding Putin for his years spent in efforts to seize Ukrainian territory.

European leaders have said Ukraine must be capable of defending itself if peace and security are to be guaranteed on the continent and that they are ready to contribute further.

"Ukraine cannot lose this war, and nobody has the right to pressure Ukraine into making territorial or other concessions, or making decisions that smack of capitulation," Polish Prime Minister Donald Tusk said at a government meeting.

"I hope we can convince President Trump about the European position."