The deal - announced on Thursday - if confirmed, would be the most significant diplomatic breakthrough yet to end the three-month-old war, which has killed thousands of people and sent global energy prices sharply higher.
Iranian media reported Foreign Ministry spokesperson Esmaeil Baghaei as saying large parts of the text under negotiation have been finalised but Iran would not compromise on its red lines.
"We have not reached a final conclusion on this matter," he said.
"This is a very important issue that is currently being reviewed by the relevant decision-making bodies."
Trump, meanwhile, told reporters at the White House: "We just made a great settlement of the war with Iran."
"The strait will officially open as soon as we sign, which could be soon, very soon, maybe over the weekend in Europe," Trump said.
When asked if Iran's Supreme Leader Ayatollah Mojtaba Khamenei approved the deal, Trump said: "I understand the answer is yes."
Trump's announcement came after he called off planned military strikes on Iran, citing progress in talks.
Since mid-March, Trump has repeatedly claimed a deal with Iran to end the war was close. The two sides traded strikes this week, straining a ceasefire announced in April.
"It's a very strong memorandum of understanding that is a little conceptual," Trump told reporters.
Trump has repeatedly said any peace deal must ensure Iran cannot develop a nuclear weapon. Iran denies it is seeking such a weapon.
Iran's demands include the lifting of international sanctions, the release of billions of dollars in frozen assets and recognition of its control of Hormuz.
The war has killed thousands of people, mainly in Iran and Lebanon, and hit the world economy by pushing up energy prices since the US and Israel launched airstrikes on Iran on February 28. In recent days, the conflict has intensified despite a tenuous ceasefire that took effect in early April.
After a US Apache helicopter was downed, Trump this week ordered new strikes around the Strait of Hormuz over two days. At the same time, Iran launched missile and drone attacks on US bases in the region.
Trump earlier on Thursday said the US would hit Iran "very hard tonight" and wanted eventually to take Iran's oil infrastructure hub Kharg Island. The island handles 90 per cent of Iran's oil exports and seizing it would give the US the ability to severely disrupt Iran's energy trade, placing enormous pressure on Tehran's economy.
The conflict has become a political headache for the White House, with polls showing Trump's approval ratings sinking amid voter anger over high gasoline prices.
Some Republicans have openly worried the war's unpopularity could cost them control of Congress in November's midterm elections. But Trump's political considerations also include satisfying Iran hawks within his Republican Party, who scuttled a prior effort, that any agreement closes Tehran's path to developing a nuclear weapon. The reaction of other Middle East powers will also be crucial.
Trump said on social media the agreement had been approved by countries including Israel, Saudi Arabia, Qatar and the United Arab Emirates.
Prime Minister Benjamin Netanyahu's office said in a statement after the Israeli leader and Trump spoke that Israel was not a party to the memorandum of understanding with Iran.
Tehran has been demanding an end to Israeli attacks in Lebanon, where fighting has continued in a parallel war between Israel and Iran-backed Hezbollah militants.
with PA
