The peace plan involves a two-tier approach with an immediate ceasefire followed by a comprehensive agreement.
Pakistan's army chief, Field Marshal Asim Munir, had been in contact "all night long" with US Vice-President JD Vance, special envoy Steve Witkoff and Iranian Foreign Minister Abbas Araqchi, a source aware of the proposals said on Monday.
Iran would not reopen the strait as part of a temporary ceasefire, a senior Iranian official told Reuters on Monday, adding that Iran would not accept deadlines as it reviewed the proposal.
Axios first reported on Sunday that the US, Iran and regional mediators were discussing a potential 45-day ceasefire as part of a two-phase deal that could lead to a permanent end to the war.
In a post laden with expletives on his Truth Social platform on Sunday, Trump threatened further strikes on Iranian energy and transport infrastructure if Iran failed to make a deal and reopen the strait by Tuesday.
Fresh aerial strikes were reported across the region on Monday, more than five weeks since the US and Israel began pounding Iran in a war that has killed thousands and damaged economies by boosting oil prices.
Iran responded to the attacks by effectively closing the Hormuz waterway, a conduit for about a fifth of the world's oil and natural gas supply, and attacking Israel, US military bases and energy infrastructure around the Gulf.
In his social media post, Trump threatened further strikes on Iranian energy and transport infrastructure that critics say would constitute a war crime.
"Tuesday will be Power Plant Day, and Bridge Day, all wrapped up in one, in Iran," he said.
"There will be nothing like it!!! Open the F***in' Strait, you crazy bastards, or you'll be living in Hell - JUST WATCH! Praise be to Allah. President DONALD J. TRUMP."
In the kind of mixed messaging that has baffled supporters, foes and financial markets alike, Trump told Fox News that Iran was negotiating, with a deal possible by Monday.
Explosions shook Tehran on Monday and a US-Israeli strike on a residential building south of the capital killed at least 13, an official told Iranian state media.
Iran fired volleys of rockets at Israel, with missile debris hitting Haifa, Tel Aviv and other spots.
Israeli rescuers retrieved two bodies from the rubble of a residential building in Haifa hit by an Iranian missile on Sunday.
In Abu Dhabi, authorities were tackling fallen debris in an industrial area after a successful interception by air defence systems.
Trump also on Sunday praised US special forces who rescued an airman in a high-risk mission deep inside Iran.
The airman, the weapons officer of an F-15 jet shot down on Friday, was wounded but "will be just fine", Trump said in a message on X.
The jet's pilot had been rescued earlier.
Under cover of darkness, US commandos slipped deep into Iran undetected to scale a 2100-metre-high ridge and took the stranded American weapons specialist to safety before dawn.
Two MC-130 aircraft that had ferried some of the roughly 100 special operations forces into rugged terrain south of Tehran suffered a mechanical failure and could not take off, a US official told Reuters.
Their commanders made a high-risk decision, ordering additional aircraft to fly into Iran to extract the group in waves.
US troops destroyed the disabled MC-130s and four additional helicopters in Iran, rather than risk leaving behind sensitive equipment.
Iran said several US aircraft were destroyed during the operation.
