Hopes of reviving peace efforts receded on the weekend when Trump scrapped a visit to Islamabad by his envoys Steve Witkoff and Jared Kushner.
Iranian Foreign Minister Abbas Araqchi shuttled to and from mediators Pakistan and Oman on Sunday before heading to Russia, where he is due to meet President Vladimir Putin.
Oil prices rose, the dollar inched higher and US stock futures wobbled lower in early Asia trade on Monday after US-Iran peace talks stalled, leaving Gulf shipping blocked.
"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 told Fox News.
"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.
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 economically vital Strait of Hormuz, which normally carries a fifth of global oil shipments, while Washington has imposed a blockade of Iranian ports.
Araqchi returned to Islamabad after holding talks on Sunday in Oman, another mediator in the war, and then headed to Russia.
Iran's envoy in Russia, Kazem Jalali, said in a post on social media platform X that Araqchi would meet with Putin "in continuation of the diplomatic jihad to advance the country's interests and amid external threats".
"Iran and Russia are present in a united front in the campaign of the world's totalitarian forces against independent and justice-seeking countries, as well as countries that seek a world free from unilateralism and Western domination," Jalali said.
Iranian state media said Araqchi discussed security in the strait with Omani leader Haitham bin Tariq al-Said and called for a regional security framework free of outside interference.
Araqchi said on X the focus of his Oman talks "included ways to ensure safe transit that is to benefit of all dear neighbours and the world."
Iran's semi-official Tasnim news agency said topics for Araqchi's talks with Pakistani officials included "implementing a new legal regime over the Strait of Hormuz, receiving compensation, guaranteeing no renewed military aggression by warmongers, and lifting the naval blockade".
Trump, speaking in Florida on Saturday, 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," he said.
Iranian President Masoud Pezeshkian told Pakistani Prime Minister Shehbaz Sharif by phone on Saturday that Tehran would not enter "imposed negotiations" under threats or blockade, an Iranian statement said.
He said the United States should first remove obstacles, including its maritime blockade, before negotiators could begin laying the groundwork for a settlement.
