Trump said a two-week ceasefire, which ends next week, could be extended, although he did not believe that would be necessary as Tehran wanted a deal.
"We're going to see what happens. But I think we're very close to making a deal with Iran," he told reporters on Thursday, adding if an agreement was reached and signed in the Pakistani capital Islamabad, he might go there for the occasion.
However, Iranian sources told Reuters some "gaps remained to be resolved" before reaching a preliminary deal.
In Islamabad, the venue of last weekend's talks, troops were seen along routes leading into the capital on Friday, but roads were still open and the government had not issued orders for businesses to shut down, as they did prior to the last meeting.
The US-Israeli attack on Iran started on February 28 and has killed thousands of people and destabilised the Middle East.
The conflict also effectively closed the Strait of Hormuz, through which a fifth of the world's oil and liquefied natural gas transits, threatening the worst oil shock in history.
The International Monetary Fund this week warned the global economy risked tipping into recession if the conflict was prolonged.
France and Britain are chairing a meeting on Friday of about 40 countries aimed at signalling to the US that some of its closest allies are ready to help restore freedom of navigation in the Strait of Hormuz, but only once hostilities cease.
Trump had called on other countries to get involved in the war and criticised NATO allies for failing to do so.
According to a note sent to invited nations, the aim of the meeting is to reaffirm full diplomatic support for unfettered freedom of navigation through the waterway and the need to respect international law.
Iran has largely closed the strait to ships other than its own, while Washington this week imposed a blockade on ships entering or leaving Iranian ports.
A Pakistani source involved in mediating between the US and Iran said on Friday there was progress in backdoor diplomacy and that an upcoming meeting between the two sides could result in the signing of a memorandum of understanding, followed by a comprehensive deal within 60 days.
One of the key sticking points has been over Tehran's nuclear ambitions, with the US proposing at last weekend's talks a 20-year suspension of all Iranian nuclear activity, while Tehran suggested a halt of three to five years.
Iran has demanded international sanctions on it be lifted and Washington has pressed for any highly enriched uranium to be removed from Iran.
Meanwhile, a US-backed ceasefire agreed between Israel and Lebanon to end the fighting between Israel and Iran-backed Hezbollah appears to be largely holding on Friday, despite some Lebanese Army reports of violations by Israel.
Mediator Pakistan said on Thursday that a parallel ceasefire in Lebanon would be an essential component of any talks on a deal to end the conflict in Iran.
The conflict in Lebanon was reignited on March 2 when Hezbollah opened fire on northern Israel in support of Tehran, prompting an Israeli offensive that authorities say has killed 2000 people.
There was no immediate comment from the Israeli military on the reported ceasefire violations on Friday.
Celebratory gunfire rang out across parts of Beirut as the clock struck midnight on Thursday to mark the start of the truce.
People uprooted by war in Lebanon began returning home on Friday, checking whether their homes were still standing amid fears over the possible fragility of the ceasefire.
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