The trip to Moscow is the second since last year for Hungarian Prime Minister Viktor Orbán, who is widely considered Putin’s closest partner among all EU leaders.
The Russian leader said he felt U.S. was taking his position into account, but some things still needed to be discussed during talks in Moscow next week.
Trump, whose envoy Steve Witkoff will visit Moscow next week, said he had no deadline for a deal after pressuring Ukraine to back a plan by Thanksgiving.
A U.S. official said Ukraine "agreed" to a deal and was sorting "minor details." Kyiv has not publicly accepted a plan and the Kremlin said it was waiting to see changes.