Putin has tried to conquer the territory for 11 years, but has failed because Ukrainian forces, deeply entrenched in the region, have repeatedly repelled his attempts. The zone is seen as a wall against a rapid Russian advance westward toward Kyiv.

Putin's focus on Donetsk suggests he is not abandoning previous demands that have stalled the talks, despite Trump's optimism about reaching a deal, said the officials, who spoke on condition of anonymity.

Russia or Russian-backed separatists have occupied part of the region since 2014, but they have never managed to conquer the entire region by force.

Trump has not publicly commented on Putin's previously unreported demand for all of Donetsk, and Trump did not endorse the Russian demand in his public statement Friday after a key meeting with Ukrainian President Volodymyr Zelensky.

He plans to meet with Putin in Hungary in the coming weeks to continue discussions about ending the war.

"Time to stop the killing and make a DEAL! Enough blood has been shed, and the boundaries of property have been set by war and courage. They should stop where they are. Let both declare victory, let history decide!" Trump wrote on social media on Friday after meeting with Zelensky.

During the Trump-Putin call, the Russian leader said he would be willing to give up parts of two other Ukrainian regions he has partially conquered, Zaporizhia and Kherson, in exchange for full control of Donetsk, officials said.

It's a slightly smaller territorial claim than the one he made during his August meeting with Trump, and some White House officials saw it as progress, said one of two senior officials briefed on Putin's call.

The Ukrainians are unlikely to see it the same way, said another official, a senior European diplomat.

"It's like selling them their own leg for nothing," the diplomat said.

Neither the White House nor the Kremlin immediately responded to a request for comment.