Trump on Friday said he would meet in a secure White House room to make a "final determination" on the proposal, which would extend an early-April truce for another 60 days, giving negotiators time to forge a permanent end to the war.
A White House official said the meeting in the Situation Room lasted about two hours, but did not address whether Trump had made a decision.
"President Trump will only make a deal that is good for America and satisfies his redlines. Iran can never possess a nuclear weapon," the official said.
A senior Iranian source told Reuters an agreement was close but had not yet been approved.
However, Trump also said Iran would have to end its chokehold on the Strait of Hormuz and dismantle its capacity to make a nuclear weapon - two conditions that Tehran has not agreed to.
"Iran must agree that they will never have a Nuclear Weapon or Bomb. The Hormuz Strait must be immediately open, no tolls, for unrestricted shipping traffic, in both directions," Trump said, adding that nuclear material would be "unearthed" by the United States.
Iran's semi-official Fars news agency, citing sources, said Trump's comments were an "attempt to portray a fabricated victory".
The senior Iranian source, speaking on condition of anonymity, said the potential deal does not include any nuclear-related issues, while Iran's Foreign Ministry spokesperson Esmaeil Baghaei said on state TV that the management of the strait must be decided by Iran and Oman.
Fars said the strait would be reopened under Tehran's conditions after the US lifts its blockade on Iranian ships.
US Treasury Secretary Scott Bessent said the US blockade would be removed slowly if it happens.
Fars said there was agreement to release $US12 billion ($A17 billion) of Iran's frozen assets.
Trump said no money would be exchanged "until further notice" - a possible reference to Iran's demands for toll payments in the strait, war damage reparations or a release of frozen Iranian assets.
Trump is under pressure to reopen the Strait of Hormuz and get US gasoline prices down ahead of the November congressional elections, as voters show increasing frustration over rising prices. At the same time, he faces a potential backlash from Iran hawks in his own party over any concessions to Tehran.
The war launched by the US and Israel on February 28 has killed thousands of people, mainly in Iran and Lebanon, and caused global economic pain by pushing up energy prices due to Iran's effective closure of the Strait of Hormuz.
In his post on Truth Social, Trump said mines would be removed from the strait and ships trapped there may start to go home: "Say HELLO to your wives, husbands, parents, and families from me, your favourite President!"
Kazakhstan has signaled it is willing to take Tehran's uranium stockpile of highly enriched uranium in the event of a deal, UN nuclear watchdog chief Rafael Grossi told the Financial Times.
Kazakhstan already hosts an internationally controlled bank of uranium to ensure fuel supplies for power stations in International Atomic Energy Agency member states. Iran also wants sanctions lifted, US forces withdrawn from the region, and for any peace deal also to end US ally Israel's offensive in Lebanon.
Israel has displaced hundreds of thousands of people and pushed deep into Lebanon as it pursues the Iran-backed Hezbollah militia.
Lebanon says more than 3200 have been killed by Israeli strikes, while Israel says 23 of its soldiers and four civilians have been killed.
