Trump has said he wants to end the Ukraine war “within a day”, but has declined to set out how this would be achieved.
Some commentators have suggested it could mean the new US administration putting pressure on Zelensky to give up some territory as part of a peace deal with Russian President Vladimir Putin.
The Ukrainian leader said he had yet to discuss the conflict with the US president-elect.
Sir Keir urged Ukraine’s allies to “step up” their backing, telling Zelensky: “As you know, our support for Ukraine is unwavering.
“It’s very important that we see this through. It’s very important that we stand with you.”
The Ukrainian president thanked him “for sticking with us all through this tough period”.
French President Emmanuel Macron and German Chancellor Olaf Scholz have also repeatedly pledged to stand by Ukraine.
Nato Secretary General Mark Rutte said Trump’s first term had stimulated Europe to spend more on defence, but “we need to do more”.
He stressed that the threat of Russia, and its alliance with North Korea, China and Iran, posed problems for the US as well as Europe.
“If Russia would be successful in Ukraine, you would have an emboldened Russia at our border,” he said in Budapest.
Rutte, who was Dutch prime minister during Mr Trump’s first 2017-2021 presidency, added: “I worked with him very well for four years.
“He is extremely clear about what he wants. He understands that you have to deal with each other to come to joint positions. And I think we can do that.”
Sir Keir dodged a question about a report Trump had privately described him as “very left-wing”.
The prime minister said their meeting in New York in September and their phone call on Wednesday after the US election result had been “very positive, very constructive”.
