Putin said U.S. allies "only have themselves to blame for what's happening," suggesting they were paying the price for opposing Trump's return to the White House.
Tensions between Zelenskyy and Trump over the new U.S. position on the war had been building for weeks.
But Zelenskyy struck a more positive tone ahead of Thursday's meeting with Kellogg, saying "it is very important for U.S. that the meeting and our work with America in general be constructive."
"Together with America and Europe, peace can be more reliable, and this is our goal," he added.
Russia, which for years has railed against the U.S. military presence in Europe, wants a reorganisation of the continent's security framework as part of any deal to end the Ukraine fighting.