The four-week war has spread across the Middle East killing thousands of people and hitting the global economy with soaring energy prices.
The United States and Israel launched strikes on Iran on February 28 after talks about Tehran's nuclear program failed to yield a deal.
On Thursday, Trump threatened during a cabinet meeting at the White House to increase pressure on Iran if it did not make a deal.
He later posted on social media that he would pause threatened attacks on Iranian energy plants for 10 days until April 6 at 8pm EDT (11am AEST on April 7).
"Talks are ongoing and, despite erroneous statements to the contrary by the Fake News Media, and others, they are going very well," he said in his Truth Social post.
Iran has said it is not engaged in talks with Washington and Trump has not identified who the US is negotiating with in Iran, with many high-ranking officials killed in the war.
On March 23, Trump announced a halt to all threatened strikes against power plants and energy infrastructure for a five-day period, but has extended it to 10 days.
Iran did not ask for a 10-day pause on such strikes, the Wall Street Journal cited peace talk mediators as saying.
Iran has said it would return strikes on energy facilities in the Gulf region if Trump follows through with his threat.
The war has massively disrupted shipping, sending crude oil prices up about 40 per cent, seen liquefied natural gas prices spike, and prices for nitrogen-based fertilisers, critical to food production, rise about 50 per cent.
Stock indices fell sharply on Thursday and Brent oil jumped to more than $US105 a barrel as hopes diminished for a quick resolution to the war.
Despite Trump's upbeat assessment, Iran continued to retaliate against US and Israeli strikes by hitting Israel and US bases.
It also struck Gulf states and effectively blocked Middle East fuel exports via the Strait of Hormuz, which carries about 20 per cent of global oil and liquefied natural gas.
Trump suggested on Thursday that Iran let 10 oil tankers transit the strait as a goodwill gesture in negotiations, including some Pakistan-flagged vessels.
Trump said the US would become the Iran's "worst nightmare" if it did not comply with US demands, which include opening the Strait of Hormuz and ending its nuclear program.
The Pentagon was looking at sending up to 10,000 additional ground troops to the Middle East, the Wall Street Journal reported.
An Iranian official told Reuters that a 15-point US proposal, conveyed to Tehran by Pakistan, was reviewed in detail by senior Iranian officials and the representative of Iran's supreme leader, who felt it served only US and Israeli interests.
The proposal included demands ranging from dismantling Iran's nuclear program to curbing its missiles and effectively handing over control of the strait, according to sources and reports.
Iran has hardened its stance since the war began, demanding guarantees against future military action, compensation for losses, and formal control of the strait, Iranian sources say.
On Thursday, Iran launched waves of missiles at Israel, striking Tel Aviv, Haifa and other areas, with a man killed in Nahariya after Hezbollah fired a rocket barrage at the northern city.
In Iran, strikes hit the southern city of Bandar Abbas and a village on the outskirts of the southern city of Shiraz, and at least six people were killed in a strike on Qom.
