Trump's statement came after Iran threatened to attack Israel's power plants and those supplying US bases across the Gulf region if the US targets Iran's power network.
Conversations with Iran will continue throughout the week, Trump said in a social media post.
A reporter for the US news outlet Axios said representatives of Turkey, Egypt and Pakistan had met White House envoy Steve Witkoff and, separately, Iranian Foreign Minister Abbas Araghchi.
Reporter Barak Ravid cited an unnamed US source as saying the discussion was about ending the war and resolving all outstanding issues.
Araghchi's ministry said there were "initiatives" to reduce tensions, the Mehr news agency reported, adding that Iran wanted the US, as the party that began the war, to be a direct participant.
The White House did not respond to questions about the content of the talks, who participated or where they were held.
A source briefed on Israel's war plans said the US had kept it informed of its talks with Iran, and that Israel was likely to follow the US in suspending any targeting of Iranian power plants and energy infrastructure.
The Israeli prime minister's office did not immediately respond to a request for comment.
The reaction from markets was swift and marked: Brent crude oil futures fell sharply, the US dollar fell against other major currencies, stock markets rallied and government borrowing costs fell back.
The United States and Iran "have had, over the last two days, very good and productive conversations regarding a complete and total resolution of our hostilities in the Middle East," Trump wrote on Truth Social on Monday.
"I have instructed the Department of War to postpone any and all military strikes against Iranian power plants and energy infrastructure for a five-day period, subject to the success of the ongoing meetings and discussions."
On Saturday, Trump warned that Iranian power plants would be destroyed if Iran failed to "fully open" the Strait of Hormuz to all shipping within 48 hours.
Trump set a deadline of 7.44 pm EDT on Monday (10.44am on Tuesday AEDT).
A spokesman for UK Prime Minister Keir Starmer on Monday welcomed the latest US statement.
"Any reports of productive talks are welcome," a spokesman said after being asked about Trump's announcement.
"We've always said that swift resolution to the war is in global interests and the Strait of Hormuz specifically needs to be reopened," the spokesman told reporters.
Iranian attacks have largely closed the Strait, which carries a fifth of global oil and liquefied natural gas.
Two Indian-flagged liquefied petroleum gas tankers on Monday sailed through the Strait although overall traffic through the waterway remained blocked, according to data and sources.
More than 2000 people have been killed in the war the US and Israel launched on February 28, which has upended markets, driven up fuel costs and fuelled global inflation fears.
The Israeli military said early on Monday it had begun its latest broad wave of strikes on infrastructure in Tehran.
Iranian news agencies said six people had been killed and 43 injured in strikes on residential buildings in the western city of Khorramabad.
A strike on the southern city of Bushehr targeted the local meteorological organisation and killed the head of meteorology for Bushehr's airport, state media reported.
The Iranian Red Crescent posted a video of a residential building in affluent northern Tehran with most of its facade destroyed and emergency staff rescuing someone on a stretcher from the upper floors.
Across the Gulf, the Saudi defence ministry said two ballistic missiles had been launched towards Riyadh.
One was intercepted while the other fell in an uninhabited area.
