Zelensky is due to fly to Washington DC on Monday to meet Trump, with the aim of paving the way to further talks.
In the wake of the Anchorage summit, Sir Keir spent Saturday morning speaking to western allies.
Following the calls, he said in a statement: “I welcome the openness of the United States, alongside Europe, to provide robust security guarantees to Ukraine as part of any deal.
“President Trump’s efforts have brought us closer than ever before to ending Russia’s illegal war in Ukraine.
“His leadership in pursuit of an end to the killing should be commended,” Sir Keir said.
Until Putin stops his “barbaric assault”, that allies would “keep tightening the screws on his war machine with even more sanctions”, he added.
France later said Sir Keir would join French President Emmanuel Macron and German Chancellor Friedrich Merz in hosting Kyiv’s allies in a video call of the “coalition of the willing” on Sunday.
A Downing Street source told the BBC that any peace deal needed security agreements and “US involvement is a key part of that”.
Following a call with Trump on Saturday, Zelensky called for a lasting peace, “not just another pause between Russian invasions”.
He stressed Kyiv should be included in future discussions, and said he expected Russia to “increase pressure and strikes” in the coming days to “create more favourable circumstances for talks with global actors”.