After 13 nights of intensifying US air strikes on Iran, the Pentagon abruptly suspended the campaign late on Friday, with no US attacks reported on either Saturday or Sunday.
Iran, which had been following each night of US attacks with its own strikes on neighbouring countries that host US bases, has also so far held fire for two days.
US ambassador to the United Nations Mike Waltz told Fox News on Sunday that Trump had decided to pause US attacks to allow more time for diplomacy.
"He's giving talks some space, he's giving it a little bit of room," Waltz said, without providing further details.
The senior Iranian source, speaking on condition of anonymity, told Reuters: "Iran's position remains 'attack for attack': if the attacks stop, Iran will also halt its operations. That message has already been conveyed to the United States."
The source added: "However, Iran is prepared to mount a broad response should the US launch another attack."
Asked about the pause, a senior official in Trump's administration said on Saturday that the president "has always been clear that his preference is diplomacy but he has shown Iran what will happen if they fail to come to the table in a serious way".
US forces had been striking Iran nightly in what the US said was retaliation for Iranian attacks on shipping in the Strait of Hormuz.
Iran says it aims to retain control of the strait, the world's most important energy shipping route.
The two-week-long US military campaign effectively torpedoed last month's interim agreement aimed at ending the war that the United States and Israel launched in February.
The New York Times and CNN both reported that Trump had backed off plans to escalate the war with even bigger military options after concerns were raised on Friday by some of his advisers, including over whether US missile defence stocks were running low from protecting US bases in the region.
CNN and the NYT both identified Pentagon Chief of Staff Dan Caine as having raised such concerns.
CNN said Vice President JD Vance also had expressed reservations.
News site Axios reported that Trump had been receiving plans for strikes on Iran from the Pentagon every afternoon for two weeks and signing off on them each night, until Friday when the latest plan was presented to him and he decided not to go ahead.
Trump's decision to pause strikes has come at a turning point in the war, with both sides testing the boundaries of escalation that they set before a ceasefire ended major fighting in April and the interim agreement reopened the Strait of Hormuz in June.
US forces have already struck bridges and tunnels in southern Iran, prompting Iran to strike water desalination plants that nearby Gulf Arab countries rely on to make their desert cities habitable.
Over the past week, Iran's Houthi allies in Yemen have announced a blockade on Saudi oil in the Red Sea, potentially shutting a second major choke point for energy shipping.
That pushed the benchmark Brent crude price above $US100 for the first time since May.
On Saturday, the Houthi militia fired on Saudi Red Sea oil targets for the first time in years.
