French President Emmanuel Macron said on Tuesday that he hoped there could be progress on Iran in the coming hours after he met leader Hassan Rouhani on Monday evening to look for common ground.
"We have to get back around the table to have a frank and demanding discussion on the nuclear activity, Iran's regional activities, the ballistic missile programme, but also to have a larger approach on what sanctions are," Mr Macron said.
"I hope we will be able to make progress in the coming hours."
Before his 90-minute meeting with Mr Rouhani, he said the biggest risk was an "uncontrolled escalation" in the Gulf.
Mr Macron then raised the attacks on Saudi Arabia's oil infrastructure with the Iranian leader.
Despite Mr Trump's harsh words, he is fond of publicity, as shown by his three meetings with North Korean leader Kim Jong-un.
Iran in recent days has sounded increasingly open to a meeting after initially ruling out any encounter with the US president.
"We are not closing the door for conversation," Iran's Foreign Minister, Javad Zarif, said on Monday at the UN.
"What we're saying is that you need to establish credibility."
Mr Zarif warned against Mr Trump using a meeting as a simple photo opportunity.
The US leader said that he appreciated the efforts of Mr Macron but he did not need a mediator.
France, initially hesitant to blame Iran for the Saudi oil attacks, joined Britain and Germany in accusing Tehran on Monday.
"It is clear to us that Iran bears responsibility for this attack. There is no other plausible explanation," Mr Macron, British Prime Minister Boris Johnson and German Chancellor Angela Merkel said after meeting at the UN. The US also blames Iran.
Iran's Foreign Ministry again rejected the accusations.
News agency Irna carried a ministry statement describing Monday's joint comments by Mr Macron, Mrs Merkel and Mr Johnson as "irresponsible and ridiculous".
