On Friday, US President Donald Trump said Ukrainian President Volodymyr Zelenskiy had until Thursday to approve the 28-point plan, which calls on Ukraine to cede territory, accept limits on its military and renounce ambitions to join NATO.
For many Ukrainians, including soldiers fighting on the front lines, such terms would amount to capitulation after almost four years of fighting in Europe's deadliest conflict since World War Two.
Since the plan was announced, there has been considerable confusion about who was involved in drawing it up. European allies said they had not been consulted.
A US official said US Special Envoy Steve Witkoff and Secretary of State Marco Rubio had arrived on Sunday for the talks on ending Russia's full-scale invasion.
"We hope to iron out the final details ... to draft a deal that is advantageous to them (Ukraine)," a US official said.
"Nothing will be agreed on until the two presidents get together," the official said, referring to Trump and Zelenskiy.
Ahead of Rubio's departure for Geneva, Trump said his current proposal for ending the war was not his final offer.
A US official said there would be co-ordination meetings on Sunday morning before talks started in earnest in Geneva.
There would be a full day of talks in different formats between US and Ukrainian officials, the official said.
Ahead of the Geneva gathering, there were also positive and constructive talks between US and Ukrainian officials, the official said, speaking on condition of anonymity.
Convoys of diplomatic vehicles shuttled through Geneva on Sunday morning as the talks were about to get under way.
US Army Secretary Daniel Driscoll was also in Geneva for the talks, while Ukraine's delegation is led by the head of Zelenskiy's office, Andriy Yermak.
National security advisers from the E3 alliance of France, Britain and Germany are joining the discussions, alongside the European Union. Italy was also sending an official.
Canadian Prime Minister Mark Carney said he would speak with Zelenskiy later on Sunday about the peace plan.
European and other Western leaders said on Saturday the US peace plan, which endorses key Russian demands, was a basis for talks to end the war but needed "additional work", as they seek a better deal for Kyiv before Thursday's deadline.
A German government source said a European draft peace plan, which is based on the US proposal, had been sent to Ukraine and to the US administration.
Before the talks, Zelenskiy warned that Ukraine risked losing its dignity and freedom - or Washington's backing - over the plan.
Russian President Vladimir Putin described the plan as the basis of a resolution to the conflict, but Moscow might object to some proposals in the scheme, which requires its forces to pull back from some areas they have captured.
with Reuters
