Iran has called for an end to the war on all fronts, including Lebanon, where US ally Israel is fighting Iran-backed Hezbollah militants. Tehran also emphasised its sovereignty over the Strait of Hormuz, demanded compensation for war damage, and an end to the US naval blockade, among other conditions.
Trump said Iran's response threatened the status of a ceasefire announced on April 7.
"I would call it the weakest right now, after reading that piece of garbage they sent us. I didn't even finish reading it," Trump, who has repeatedly threatened to end the ceasefire, told reporters.
The US had proposed an end to fighting before starting talks on more contentious issues, including Iran's nuclear program. In Washington, the Pentagon put the cost of the war at $US29 billion ($A40 billion) so far, an increase of $US4 billion ($A5.5 billion) from an estimate provided late last month.
Brent crude oil futures extended gains on Tuesday, climbing to almost $US108 ($A149) a barrel, as the deadlock left the Strait of Hormuz largely closed. Before the war began on February 28, the narrow waterway carried a fifth of the world's oil and liquefied natural gas shipments, and has since become a central pressure point in the conflict.
US Central Command said the aircraft carrier Abraham Lincoln was in the Arabian Sea continuing to enforce the US blockade against Iran, having redirected 65 commercial vessels and disabled four.
US ally Kuwait announced the arrest of four infiltrators affiliated with Iran's Revolutionary Guards after they attempted to enter the Gulf state by sea, according to the state news agency KUNA, citing the interior ministry. There was no immediate reaction from Iran to the report.
Iranian officials meanwhile issued statements signalling continued resolve in the face of US pressure.
In a post on X, parliamentary national security and foreign policy commission spokesperson Ebrahim Rezaei said Iran could enrich uranium up to 90 per cent purity, a level considered weapons-grade, if the country is attacked once more.
In Iran's capital Tehran, the Guards held drills "centred on preparation to confront the enemy", state TV reported.
The US on Monday imposed new sanctions on individuals and companies it said were helping Iran ship oil to China, part of efforts to cut off funding for Tehran's military and nuclear programs, while also warning banks about attempts to evade existing curbs.
Trump is expected to arrive in Beijing on Wednesday, where Iran is set to be among the topics discussed with Chinese President Xi Jinping.
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 an Iranian attack.
In the US, surveys show the war is unpopular with US voters who are paying more for fuel less than six months before nationwide elections that will determine whether Trump's Republican Party retains control of Congress.
Two out of three Americans, including one in three Republicans and almost all Democrats, think Trump has not clearly explained why the country has gone to war, according to a Reuters/Ipsos poll completed on Monday.
Trump said he would suspend the federal tax on petrol until it was "appropriate", to help reduce fuel prices.
"As soon as this is over with Iran, as soon as it's over, you're going to see gasoline and oil drop like a rock," he said.
In the Qatari capital Doha, visiting Turkish Foreign Minister Hakan Fidan said his country supported efforts to reopen the Strait of Hormuz and added that the channel should not be used as a "weapon" during the Iran war.
Washington has struggled to build international support, with NATO allies refusing to send ships to reopen the waterway without a full peace deal and an internationally mandated mission.
