David Cameron is to meet Iranian President Hassan Rouhani in an attempt to persuade his country to join action against Islamic State (IS).
The New York meeting comes after the US and its allies began air strikes against IS in Syria, but the proposed nature of Iranian action is unclear.
It will be the first time a UK prime minister has met an Iranian president since the Iran's revolution in 1979.
Meanwhile, the UK government said it had not joined Syria strikes "yet".
Mr Cameron and Mr Rouhani spoke by phone in November, but the talks later will be their first face-to-face meeting.
BBC United Nations correspondent Nick Bryant said relations between the UK and Iran had "thawed considerably" in recent months.
"Coming at a time when the Obama administration has said Iran has a role to play in combating IS, Mr Cameron is expected to gauge what form that might take," he said.
Mr Cameron is also likely to press Mr Rouhani to withdraw support for the Assad regime in Syria - a "hard sell", our correspondent added.
He said Iranian officials in the US had raised the possibility of a "trade-off" under which Iran could get concessions on advancing its nuclear programme in exchange for "further action" against IS - though the US has said the two issues are entirely separate.
'Not ruled out'
The US has been carrying out air strikes against IS militants in Iraq since August, and the Pentagon has now announced similar action in Syria.
Rear Adm John Kirby said: "I can confirm that US military and partner nation forces are undertaking military action against Isil terrorists in Syria using a mix of fighter, bomber and Tomahawk land attack missiles."
Asked if the UK was one of those "partner" nations, a Ministry of Defence spokeswoman told the BBC: "The UK has not committed anything yet. Conversations are ongoing.
"There might potentially be an update in the coming days. We have not ruled ourselves out."
Jihadist group IS, also referred to as Isil and Isis, has taken control of large areas of Iraq and Syria in recent months.