KYIV, Ukraine—Thousands protested across Ukraine against President Volodymyr Zelensky’s efforts to end a five-year conflict with Russia, adding a domestic challenge to a novice leader who is also trying to contain fallout from his phone call with President Trump.

Protesters worry that Mr. Zelensky—encouraged by European leaders eager to improve ties with Russia—is acceding to Moscow’s demands. The Kremlin wants to reintegrate separatist regions it controls, starting with holding elections in the region of eastern Ukraine. That, the critics say, could allow Moscow to disrupt Kyiv’s plans to integrate Ukraine with the West.

“It’s a foot in the door for Russia in Ukraine,” said Danylo Kovzhun, a 43-year-old computer scientist, at a protest on Sunday.

Mr. Zelensky swept to the presidency in an April election with a promise to end the conflict, which has cost some 13,000 lives and sapped Ukraine’s limited resources. In recent weeks, Mr. Zelensky’s administration has been sucked into the storm in U.S. politics over Mr. Trump’s requests that Ukraine open an investigation into his Democratic rival, Joe Biden, and his son.

That situation has barely resonated in Kyiv. Mr. Zelensky’s administration has focused on efforts to end the conflict with Russia, which covertly sent armed forces into eastern Ukraine in 2014 and set up two separatist statelets.