Iran and "other Middle Eastern Countries" asked for a time to complete a deal that would lead to "the Immediate, Complete and Total" reopening of the Strait and "an end to Iran's nuclear threat," Trump wrote on his Truth Social platform on Saturday.
"Based on this request, I have agreed, for the future benefit of the WORLD and, likewise, the survival of a successful and prosperous Iran, to cancel the attack, subject to being able to rapidly make a DEAL." Israel "joins me in this commitment," Trump wrote.
Israel did not immediately make a public statement on the issue.
Iran warned the US this weekend against any "adventurous action" and said it would retaliate decisively if American forces followed through on Trump's threats of fresh attacks on Iranian targets.
Iranian Foreign Minister Abbas Araqchi's comments in separate phone calls on Saturday with senior Turkish, Pakistani and Saudi officials came just hours after Kuwait's army said it destroyed hostile drones launched by Iran against several vital facilities.
Speaking to Pakistan's Army Chief Field Marshal Asim Munir and Turkish Foreign Minister Hakan Fidan, Araqchi said Iran would respond decisively to any "aggression" and discussed the consequences of "destabilising actions" by the US, as well as prospects for heightened regional insecurity, according to Araqchi's Telegram account.
Araqchi later told Saudi Foreign Minister Prince Faisal bin Farhan that any attacks by the US and Israel or participation by regional countries in such actions would be met with a "proportionate response".
Saudi Crown Prince Mohammed bin Salman spoke to Trump on Saturday and "expressed concern and asked for clarity" about US plans for Iran, a US official told Axios.
The Saudi crown prince spoke to Trump, a White House official told Reuters, but did not provide details.
Nournews, a media outlet affiliated with Iran's top security body, said on Saturday that US attacks on Iranian energy infrastructure would prompt Iranian strikes on oil fields in Saudi Arabia and the United Arab Emirates, as well as the gas fields of Qatar and Israel, saying, "all will be burned to ashes".
At a cabinet meeting on Friday at the Camp David retreat, Trump said he believed US negotiators, including his son-in-law Jared Kushner, special envoy Steve Witkoff and Secretary of State Marco Rubio, could still reach a deal with Iran.
But Trump also said he was losing faith in the Iranians, saying:"They break their word so often" - a claim Tehran has frequently levelled at Washington - and said he would be "hitting them".
Oil prices have stayed high since US and Israeli forces started the war with strikes on Iran on February 28.
Trump has argued that his stated goal of keeping Iran from gaining nuclear weapons justifies higher fuel costs in the near term, but the economic pain has put political pressure on him to find a way to end the war. Benchmark Brent crude futures rose 24 per cent in July, and analysts polled by Reuters expect prices to rise further this year.
The risk of Iranian attacks has deterred most shipping through the Strait of Hormuz, an important conduit for global energy supplies, since the start of the conflict, sending shockwaves through the world economy.
A government facility in northern Kuwait and civilian property belonging to a company on Bubiyan Island were hit on Saturday, with falling shrapnel causing material damage but no casualties, the Kuwaiti army said.
Adding to the energy industry's concerns, Iran's Houthi allies in Yemen recently began threatening the Bab el-Mandeb, the strait at the other end of the Red Sea from the Suez Canal, another export route for Saudi crude.
The United Kingdom Maritime Trade Operations said on Saturday it had received reports of two maritime incidents off Oman, including one in which a tanker was struck by an unknown projectile that damaged the engine room.
In the other incident, the master of a tanker reported seeing a large splash and an explosion close to the vessel, though no damage was reported.
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