By Maia Davies, BBC News, Mar.12: Ukraine has said it is ready to accept an immediate 30-day ceasefire with Russia proposed by the US, after a day of US-Ukraine talks in Saudi Arabia.
US Secretary of State Marco Rubio said he would present the offer to Russia and that "the ball is in their court".
Ukraine's President Volodomyr Zelensky said it was now up to the US to convince Russia to agree to the "positive" proposal.
Tuesday's talks in Jeddah were the first official meeting between the two countries since the extraordinary clash between Zelensky and US President Donald Trump in the Oval Office on 28 February.
In a joint statement, the US also said it would immediately restart intelligence sharing and security assistance to Ukraine, which Washington had suspended after the unprecedented public row at the White House.
"Both delegations agreed to name their negotiating teams and immediately begin negotiations toward an enduring peace that provides for Ukraine's long-term security," the US-Ukraine statement said.
Rubio told a press conference in Jeddah late on Tuesday that he hoped Russia would accept the proposal.
Ukraine was "ready to stop shooting and start talking," he said, and if Russia rejected the offer "then we'll unfortunately know what the impediment is to peace here".
"Today we made an offer that the Ukrainians have accepted, which is to enter into a ceasefire and into immediate negotiations," he said.
"We'll take this offer now to the Russians and we hope they'll say yes to peace. The ball is now in their court," he added.
The offer of a 30-day ceasefire goes beyond Zelensky's proposal for a partial truce in the sky and at sea.
The Ukrainian president thanked Trump for "the constructiveness" of the talks in Jeddah.
In a video message, Zelensky said Russia had to "show its willingness to stop the war or continue the war".
"It is time for the full truth," he added.
The Kremlin has not yet publicly responded. It said earlier on Tuesday it would issue a statement after being briefed by Washington on the outcome of the talks.
But influential Russian lawmaker Kostantin Kosachev said that any potential agreements would be "on our terms, not American".
Kosachev, chairman of the Federation Council's international affairs committee, said "real agreements are still being written... at the front", stressing that Russian troops were advancing in Ukraine.
Russia launched a full-scale invasion of Ukraine in February 2022. Moscow currently controls about 20% of Ukrainian territory.
At the White House, Trump told reporters he would speak with Russian President Vladimir Putin, who would "hopefully" agree to the proposal.
"It takes two to tango, as they say," Trump said, adding he hoped the deal would be agreed in the next few days.
"We have a big meeting with Russia tomorrow, and some great conversations hopefully will ensue."
He added that he was open to inviting Zelensky back to Washington.
reign Ministry spokeswoman Maria Zakharova said Russia had not ruled out talks with US representatives in the next few days, according to Russia's state-owned news agency Tass.
Asked by a reporter if Trump and Zelensky's relationship was "back on track," Rubio said he hoped it was "peace" that was back on track.
"This is not Mean Girls, this is not some episode of some television show," he said.
"Today people will die in this war, they died yesterday and - sadly - unless there's a ceasefire, they will die tomorrow."
The US and Ukrainian teams met after overnight drone attacks killed at least three people in near Moscow - which Russia said showed Ukraine had rejected using diplomacy to end the war.