Iranian sources earlier on Monday disclosed Iran's latest proposal, which would set aside discussion of its nuclear program until the war is ended and disputes over shipping from the Gulf are resolved.
That is unlikely to satisfy the United States, which says nuclear issues must be dealt with from the outset.
Secretary of State Marco Rubio said he thought Iran was trying to buy more time.
"We can't let them get away with it," he said in an interview with Fox News.
"They're very good negotiators. They're very experienced negotiators. We have to ensure that any deal that is made, any agreement that is made is one that definitely prevents them from sprinting toward a nuclear weapon at any point," Rubio said.
Work to bridge gaps between the United States and Iran has not halted, sources from mediator Pakistan said, despite the absence of face-to-face diplomacy after Trump called off a trip by his representatives over the weekend.
Hopes of reviving peace efforts have receded since the US president this weekend announced he had scrapped a visit by his special envoy Steve Witkoff and son-in-law Jared Kushner to Islamabad, the Pakistani capital, where Iranian Foreign Minister Abbas Araqchi shuttled in and out twice during the weekend.
Araqchi also visited Oman and on Monday went to Russia, where he met President Vladimir Putin and received words of support from a longstanding ally.
With the warring sides still seemingly far apart on issues including Iran's nuclear ambitions and access to the crucial Strait of Hormuz, oil prices resumed their upward march on Monday, hitting a two-week high.
Trump met his national security team on Monday morning.
"There was a discussion this morning that I don't want to get ahead of, and you'll hear directly from the president, I'm sure, on this topic very soon," White House spokeswoman Karoline Leavitt said.
Araqchi told reporters in Russia that Trump had requested negotiations because the US has not achieved any of its objectives.
Senior Iranian sources, speaking on condition of anonymity, told Reuters the proposal carried by Araqchi to Islamabad over the weekend envisioned talks in stages, with the nuclear issue to be set aside at the start.
A first step would require ending the US-Israeli war on Iran and providing guarantees that the United States cannot start it up again.
Then negotiators would resolve the US blockade and the fate of the Strait of Hormuz, which Iran aims to reopen under its control.
Only then would talks look at other issues, including the longstanding dispute over Iran's nuclear program, with Iran still seeking some kind of US acknowledgement of its right to enrich uranium for what it says are peaceful purposes.
In a sign that no face-to-face meetings are planned any time soon, streets reopened in Pakistan's capital Islamabad, which had been locked down for a week in anticipation of talks that never took place.
Pakistani officials said negotiations were still taking place remotely but there were no plans to convene a meeting in person until the sides were close enough to sign a memorandum.
Fighting has intensified in Lebanon, where Israeli strikes killed 14 people and wounded 37 in the south on Sunday, according to the health ministry, making it the deadliest day since a US-brokered ceasefire was announced in mid-April.
Iran says it will not hold talks on the wider conflict unless a ceasefire also holds in Lebanon, which Israel invaded in March in pursuit of the militant group Hezbollah which fired across the border in solidarity for Iran.
Israel and Hezbollah blame each other for violating the truce agreed between Israel and the Lebanese government in the US and extended last week.
