Hopes of reviving peace efforts receded on Saturday 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 flying to Russia, with the two sides still seemingly far apart on issues including Iran's nuclear ambitions and access through the crucial Strait of Hormuz.
Oil prices rose and US stock futures wobbled lower in early Asia trade on Monday after US-Iran peace talks stalled at the weekend, 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."
Iran has long demanded Washington acknowledge its right to enrich uranium, which Tehran says it seeks only for peaceful purposes, but which Western powers 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.
Axios reported on Sunday that Iran gave the US a new proposal through Pakistani mediators on reopening the economically vital Strait of Hormuz and the ending of the war, with nuclear negotiations postponed for a later stage.
With his approval ratings falling, Trump faces domestic pressure to end the unpopular war.
Iran's leaders, though weakened militarily, have found leverage in negotiations with their ability to stop shipping in the strait, which usually carries a fifth of global oil shipments.
Tehran has largely closed the strait 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, posted on X that Araqchi would meet 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.
While Araqchi met Pakistani officials, Trump 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.
Disagreements between the US and Iran extend beyond Tehran's nuclear program and control of the strait.
Trump wants to limit Iran's support for its regional proxies, including Hezbollah in Lebanon and Hamas in Gaza, and curb its ability to strike US allies with ballistic missiles.
Iran wants a lifting of sanctions and an end to Israeli attacks on Hezbollah.
In Lebanon, Israeli strikes killed 14 people and wounded 37 on Sunday, the health ministry said.
The Israeli military warned residents to leave seven towns beyond the "buffer zone" it occupied before a ceasefire that has failed to fully halt hostilities.
