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 that began 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.
Brent crude oil futures extended gains in early Asian trade on Tuesday, climbing above $US104.50 a barrel, as 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 shipments, 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.
The United States 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.
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.
Washington has also 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.
In separate statements on Monday, the State Department said US Secretary of State Marco Rubio held separate calls with his Australian and British counterparts to discuss "ongoing efforts to restore freedom of navigation in the Strait of Hormuz".
It did not elaborate.
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, would hold talks in Qatar on Tuesday on the conflict and on ensuring navigational safety in the strait, a Turkish diplomatic source said.
