Hopes of reviving peace efforts had earlier receded after Trump scrapped a visit to Islamabad by his envoys Steve Witkoff and Jared Kushner, even as Iranian Foreign Minister Abbas Araqchi continued to shuttle between mediating countries.
"If they want to talk, they can come to us, or they can call us. You know, there is a telephone. We have nice, secure lines," Trump said in an interview on Fox News on Sunday.
"They know what has to be in the agreement. It's very simple: they cannot have a nuclear weapon, otherwise there's no reason to meet," Trump said.
Iran has long demanded Washington acknowledge its right to enrich uranium, which Tehran says it only seeks for peaceful purposes but which Western powers and Israel say is aimed at building nuclear weapons.
Although a ceasefire has paused full-scale fighting in the conflict, which began with US-Israeli strikes on Iran on February 28, no agreement has been reached on terms to end a war that has killed thousands, driven up oil prices, fuelled inflation and darkened the outlook for global growth.
Tehran has largely closed the Strait of Hormuz, which normally carries a fifth of global oil shipments, while Washington has imposed a blockade of Iran's ports.
After holding talks in Pakistan, Araqchi flew to Oman - another mediator in the war - where he met the country's leader, Haitham bin Tariq al-Said, on Sunday.
They discussed security in the strait and Araqchi called for a regional security framework free of outside interference, according to Iran's foreign ministry.
Araqchi later returned to Islamabad, Iranian state media reported. Pakistani government sources said he would hold talks with the country's leadership before heading to Moscow.
Iran's semi-official Tasnim news agency reported that Araqchi's talks with Pakistani officials would include "implementing a new legal regime over the Strait of Hormuz, receiving compensation, guaranteeing no renewed military aggression by warmongers, and lifting the naval blockade."
The talks would be unrelated to Iran's nuclear program, the report said.
Speaking in Florida before being rushed out of the White House Correspondents' Association dinner in Washington when a man opened fire nearby, Trump said he cancelled his envoys' visit due to too much travel and expense for what he considered an inadequate Iranian offer.
Iran "offered a lot, but not enough," Trump said.
An earlier round of talks in Islamabad - in which Vice President JD Vance led the US delegation opposite Iran's parliamentary speaker Mohammad Baqer Qalibaf - ended without agreement.
After the latest diplomatic trip was called off, two US Air Force C-17s carrying security staff, equipment and vehicles used to protect US officials flew out of Pakistan, two Pakistani government sources told Reuters on Sunday.
Iranian President Masoud Pezeshkian told Pakistani Prime Minister Shehbaz Sharif by phone that Tehran would not enter "imposed negotiations" under threats or blockade, according to a statement from the Iranian government.
He said the United States should first remove obstacles, including its maritime blockade, before negotiators could begin laying the groundwork for a settlement.
Writing on Truth Social before the shooting at the White House Correspondents' Dinner, Trump said there was "tremendous infighting and confusion" within Iran's leadership.
Pezeshkian said last week there were "no hardliners or moderates" in Tehran and that the country stood united behind its supreme leader.
The war has destabilised the Middle East - Iran has struck its Gulf neighbours and conflict between Israel and Iran-backed Hezbollah in Lebanon has been reignited.
Israel's military issued new evacuation orders for southern Lebanon on Sunday, ordering residents to leave seven towns beyond the "buffer zone" it occupied before a ceasefire that has failed to bring a full halt to hostilities.
