President Vladimir V. Putin of Russia has shifted President Trump’s attention back to President Volodymyr Zelensky of Ukraine by making a proposal for territory that is fraught with security and political risk for Kyiv.

Along with other demands, Mr. Putin proposed that Ukraine hand over the remainder of the Donbas region to Moscow, and in exchange Russia would stop fighting along the rest of the front, Mr. Trump told European leaders in a call after meeting with Mr. Putin in Alaska. Mr. Trump backed the idea of Ukraine’s ceding territory to freeze the war.

In a meeting on Monday at the White House, Mr. Zelensky will be forced to contend with the Russian proposal and the possibility that Mr. Trump could return to viewing him as an obstacle to peace.

After the Alaska summit Friday, Mr. Trump said it would be up to Mr. Zelensky, who has rejected the idea of ceding territory outright, to make a deal to end the war.

“It’s a very smart ploy by Putin,” said Alexander Gabuev, director of the Carnegie Russia Eurasia Center. Mr. Gabuev said the proposal could be a “poison pill” designed to weaken Ukraine internally or get Mr. Trump to walk away from Mr. Zelensky if he refuses.

Ukraine’s Constitution bars ceding territory apart from through a nationwide referendum. A recent poll by the Kyiv International Institute of Sociology found that 78 percent of Ukrainians were against transferring territory controlled by Ukraine to Russia.