Sir Keir Starmer has said he hopes to meet Kamala Harris and Donald Trump before the US election.
The prime minister, speaking from a flight to the US for the annual United Nations General Assembly (UNGA), said it would be "very good to meet both of them at some stage before the election".
"We'll just have to see what's possible," he added.
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Sir Keir flew to New York on Tuesday night after giving his keynote speech at the Labour Party conference, his first since becoming prime minister.
During his speech he defended cutting winter fuel payments to 10 million pensioners and said his government would turn the country's fortunes around but warned of a "hard" path ahead.
He will meet fellow world leaders in New York, and is likely to see US President Joe Biden and his vice president Ms Harris, which could make it diplomatically awkward only to meet one of the presidential candidates.
However, Mr Trump's campaign schedule could make arranging a meeting complicated.
Focus at the UNGA will be on the Ukraine war and the escalating situation in the Middle East.
On the way to New York, Sir Keir told Britons in Lebanon to "leave immediately" as he announced about 700 British troops have been deployed to Cyprus in case an emergency evacuation is needed.
Thousands of British nationals are in Lebanon, where at least 560 people were killed and about 2,000 injured on Monday and Tuesday in a wave of Israeli strikes.
Tens of thousands of people have been forced to flee their homes in southern Lebanon as Israel says it is targeting Hezbollah personnel.
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On Wednesday morning, Hezbollah launched a missile at Tel Aviv in its deepest strike yet into Israel, marking a further escalation of the conflict that has spread from Gaza.
The Israeli military said it intercepted the missile, which set off air raid sirens in Tel Aviv and across central Israel. There were no reports of casualties or damage.
Hezbollah said it fired a ballistic missile targeting the headquarters of Israel's Mossad intelligence agency, which it blames for a recent string of killings of its top commanders and for last week's attack in which explosives in pagers and walkie-talkies killed dozens of people and wounded thousands.
Read more from Sky News:
Terrified families flee homes in Lebanon
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Tap hereUkrainian President Volodymyr Zelenskyy is also at the UN meeting, with Sir Keir saying discussions will take place about the issue of whether British long-range ballistic missiles can be used to fire into Russia.
They will also discuss Mr Zelenskyy's "victory plan" which he will present to the White House this week but is being kept under wraps until then.
Asked about the plan and if there will be an update on the missiles, Sir Keir said: "I do think it's going to take quite a bit of time at the UN General Assembly. And I think that's really important because it's at a critical stage.
"Obviously, President Zelenskyy has a plan that he wants to walk through with all of us, and we knew that was going to happen.
"The support for Ukraine is resolute. We supply quite a lot of capability already under the last government; we've increased that under this government - that's not a criticism of the last government - and we will always listen very carefully to what Ukraine says it needs by way of capability."
He added: "I don't think that will be a discussion, I don't think the victory plan will be about a sole issue like long-range missiles, it will be about a strategic, overarching route for Ukraine to find a way through this and succeed against Russian aggression."
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