Days after the United States floated a proposal aimed at reopening negotiations, Iran on Sunday released a response focused on ending the war on all fronts, including Lebanon, where US ally Israel is fighting Iran-aligned Hezbollah militants.
The response had been swiftly rejected by Trump.
Asked where the ceasefire stands, Trump told reporters on Monday.
"I would call it the weakest right now, after reading that piece of garbage they sent us. I didn't even finish reading it," he said.
In its response, Iran also demanded compensation for war damage, emphasised its sovereignty over the Strait of Hormuz and called on the US to end its naval blockade, guarantee no further attacks, lift sanctions and remove a ban on Iranian oil sales.
Two regional officials told the Associated Press that Iran offered to dilute part of its highly enriched uranium and transport the rest to a third country.
The US had proposed an end to fighting before starting talks on more contentious issues, including Iran's nuclear program.
Iran defended its stance on Monday.
"Our demand is legitimate: demanding an end to the war, lifting the (U.S.) blockade and piracy, and releasing Iranian assets that have been unjustly frozen in banks due to U.S. pressure," foreign ministry spokesman Esmaeil Baghaei said.
"Safe passage through the Strait of Hormuz and establishing security in the region and Lebanon were other demands of Iran, which are considered a generous and responsible offer."
Brent crude oil futures traded 2.7 per cent higher at about $US104 a barrelas the deadlock left the Strait of Hormuz largely closed.
Before the war began on February 28, the narrow waterway carried one-fifth of the world's oil and liquefied natural gas, and has since become a central pressure point in the conflict.
Disruption caused by the near-closure of the strait has forced oil producers to cut exports, and OPEC oil output dropped further in April to the lowest in more than two decades, a Reuters survey showed on Monday.
Traffic through the Strait of Hormuz is at a trickle compared with before the war.
Shipping data on Kpler and LSEG showed that three tankers laden with crude exited the waterway last week, with trackers switched off to avoid Iranian attack.
A second Qatari LNG tanker was attempting to transit the strait, the data showed, days after the first such cargo crossed under an arrangement involving Iran and Pakistan.
Hakan Fidan, the foreign minister of Turkey, which has been liaising closely with the US, Iran and mediator Pakistan since the start of the war, will hold talks in Qatar on Tuesday on the conflict and on ensuring navigational safety in the strait, a Turkish diplomatic source said.
The next diplomatic or military steps remain unclear.
Trump is expected to arrive in Beijing on Wednesday, where Iran is set to be among the topics discussed with Chinese President Xi Jinping.
Trump has been leaning on China to use its influence to push Iran toward a deal with the US.
with AP
