The UK's prime minister has held talks with the Iranian president for the first time since Iran's 1979 revolution.
David Cameron and Hassan Rouhani's meeting in New York is being taken as a sign of a thawing of relations.
It came after the US and five Gulf and Middle East countries began bombing Islamic State (IS) militants in Syria.
The UK parliament is expected to be recalled on Friday to discuss taking part in military action in Iraq.
US Secretary of State John Kerry has said Iran, which supports Bashar al-Assad's government in Syria, has a role to play in the fight against IS.
But Iran's leaders have questioned the US's intentions and have argued that air strikes will not eliminate the threat from IS.
Relations between the UK and Iran have improved in recent months, with the UK government announcing in June that it was to re-open its embassy in Tehran. It closed after it was stormed in 2011.
Tensions also remain over Iran's uranium-enrichment programme, which it insists is for energy purposes, but the UK and other countries say could be used to build weapons.