Donald Trump and Volodymyr Zelenskyy are set to hold talks over the Ukraine peace plan.
US and Ukrainian officials have held discussions in Geneva about a controversial 28-point proposal drawn up by America and Russia, which has since been countered by an amended deal drawn up by Kyiv's European allies.
The White House said there were still a "couple of points of disagreement" as of Monday night, but spokeswoman Karoline Leavitt said there was a "sense of urgency" to strike an agreement.
"The president wants to see this deal come together, and to see this war end," she added.
Mr Zelenskyy echoed that message, saying "there is still work for all of us to do to finalise the document".
"We must do everything with dignity," he said in his nightly video address, adding: "The sensitive issues, the most delicate points, I will discuss with President Trump."
It comes after Mr Trump, who had accused Ukraine of not being grateful enough for US military support while the Geneva talks were under way, suggested the process could be moving in the right direction.
He had earlier given Kyiv until Thursday to agree to the plan, but US Secretary of State Marco Rubio downplayed the deadline, saying officials could keep negotiating.
Moscow, however, has already signalled its opposition to the European version of the peace plan.
It would halt fighting at present front lines, leaving discussions of territory for later, and also include a NATO-style US security guarantee for Ukraine.
Read more:
Trump's 28-point peace plan in full...
...and Europe's 28-point counterproposal
The talks in Geneva, Switzerland, had begun with Mr Rubio denying the original plan was written by Russia.
It appeared to include a number of longstanding Kremlin demands that have proved impossible for Kyiv, including sacrificing territory Russian forces have not even seized since the war began.
Ms Leavitt has also insisted the US is not favouring the Russians.
Starmer to lead talks of Ukraine's allies
Ukraine's allies in the so-called "coalition of the willing" will hold a virtual meeting today, chaired by Sir Keir Starmer.
The British prime minister said the alliance was focused on achieving a "just and lasting peace".
It "matters for all of us, because the conflict in Ukraine has had a direct impact here in the UK", he added.
The meeting will get under way hours after Russian drone strikes in Kyiv left triggered fires on residential buildings, forcing evacuations and leaving several people injured.
The war was also a topic of discussion in a call between Mr Trump and China's Xi Jinping on Monday.
Mr Xi urged "all parties" in the conflict to "reduce differences", according to Chinese state news agency Xinhua.
He reiterated that China supported all efforts conducive to peace.
China has remained a consistent ally of Russia throughout its invasion of Ukraine, and is the top buyer of Russian oil, along with India.
(c) Sky News 2025: Russian drones strike Kyiv as Zelenskyy eyes talks with Trump over 'delicate' peace plan
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