Russia has in recent weeks intensified its deadly missile and drone attacks on Kyiv and other Ukrainian cities

Ukraine's capital has come under a new missile attack, hours after Russia said it was "ready in principle" to resume peace talks and the US president said the world was "the closest we've been" to ending the war.

Several houses were hit in the attack, injuring six people, Kyiv Mayor Vitaliy Klitschko said.

The attack came amid a new diplomatic push led by US President Donald's Trump's envoys Steve Witkoff and Jared Kushner. Witkoff met Russia's President Vladimir Putin in the city of St Petersburg on Wednesday - a day after meeting Ukraine's leader.

Three-way talks were paused in February, after which Russia stepped up attacks as Ukraine ran out of Western-supplied interceptors to defend against missiles.

Putin launched a full-scale invasion of Ukraine in 2022, and Moscow currently controls about 20% of Ukrainian territory.

Rosenberg: US diplomatic push offers little hope for imminent Ukraine peace

Speaking on Wednesday, Trump said: "The other day I was talking to Vladimir Putin about settling his war with Ukraine, which I think we're getting closer to, by the way, maybe now the closest we've been."

The US president has so failed to bring the Russia-Ukraine war to an end despite his repeated comments that he would be able to achieve this.

Trump's special envoy Witkoff went to St Petersburg after meeting Ukraine's President Volodymyr Zelensky as well as the leaders of Norway and Finland in the Norwegian capital, Oslo, on Monday.

It is not clear what specific proposals Witkoff brought to Putin, but Zelensky said after talks in Oslo that "strong" security guarantees for Ukraine and energy ceasefire proposals had been discussed.

Putin's aide Yuri Ushakov said their ideas were not very "useful".

Top officials from Russia, Ukraine and the US have held several rounds of talks aimed at ending the war.

Russia blamed last month's "massive" Ukrainian strikes during its general elections for their disruption.

The latest talks between Putin (right) and Witkoff lasted about three hours in St Petersburg

Speaking to reporters after Wednesday's talks in St Petersburg, Ushakov suggested that a new round could be held around 10 November in Abu Dhabi, the capital of the United Arab Emirates.

He stressed that the talks must focus on "building a security system for Russia and Ukraine after the end of the conflict."

Ushakov also told reporters that President Putin reiterated to Witkoff that Russian troops were advancing everywhere across the vast front line and had a "strategic initiative".

Ukraine and its European allies are disputing Putin's claim, pointing to a virtual stalemate on the front.

On Wednesday, Zelensky said he would accept a deal that would freeze the war along the current front line.

"We call it 'ceasefire' or 'stop killings' like President Trump called it. Freeze and stop. And of course this is minimum what we need from Russia today," he told Fox News, adding that security guarantees for Ukraine could be discussed after this.

Watch: Zelensky says US military intelligence sharing "works now"

Witkoff described the latest talks as "constructive", while Kushner, who was participating via a video link, said: "There is still hard work ahead, but we have a real opportunity to move beyond this war and build a framework for lasting peace, security, and prosperity for generations to come."

The talks were held amid a growing row between Ukraine and the US.

Trump has said it is time for Ukraine to get a new president, and most recently "for somebody else to negotiate on behalf of Ukraine".

Trump has blamed Ukraine's attacks on Russian oil refineries for fuel prices which have been rising since the start of the US-led war on Iran.

He was heavily criticised by Democratic and some Republican lawmakers after lifting sanctions on Russia - allowing it to release tonnes of diesel "to the American and global marketplace".

That was despite signing legislation to authorise fresh US sanctions and tariffs on nations that import Russian oil and gas just weeks earlier.

Zelensky - and Ukraine's European allies - criticised Trump's move.

Last week, Kyiv accused Washington of withholding critical intelligence to warn Ukrainians about incoming Russian ballistic missile launches, resulting in many civilian deaths. US Secretary of State Marco Rubio on Tuesday rejected such accusations as "scandalous", and Zelensky said after the Oslo talks that intelligence sharing "works now".

Ukraine's military has also complained of speed restrictions by the US satellite internet network Starlink which is owned by Elon Musk which constricted its ability to use drones to conduct strikes against Russia.

US officials have denied having requested such a slowdown and a bipartisan group of US senators has called for an urgent investigation.

Hubbard had been in jail in Russia for allegedly fighting for Ukraine

Before the Putin-Witkoff talks started, Russia released Stephen Hubbard, a 74-year-old American citizen who had been given a jail sentence of nearly seven years for allegedly fighting on behalf of Ukraine.

Trump said the former teacher was "on his way back home" and "there was no 'swap' necessary", while Witkoff called Putin a "humanitarian" for agreeing the release.

When asked by a BBC reporter whether he agreed with such description of the Kremlin leader, US Vice-President JD Vance said: "I agree with Steve Witkoff saying something nice to a person who just released an American hostage.

"Whether you agree with the underlying sentiment or not, Steve Witkoff is a diplomat. His job is to go over there and get a job done. I care much less about what Steve said and about the fact that he is bringing an American hostage home to his family."

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US citizen Stephen Hubbard freed by Russia as Trump envoy meets Putin