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 demanded compensation for war damage, an end to the US naval blockade, a guarantee of no further attacks, and resumption of Iranian oil sales.
Tehran also emphasised its sovereignty over the Strait of Hormuz, where it has shut down shipping traffic that normally carries one-fifth of the world's oil and gas supply.
Trump on Monday said Iran's response threatened the status of a ceasefire that has been in place since Thursday.
"I would call it the weakest right now, after reading that piece of garbage they sent us. I didn't even finish reading it," said Trump, who has repeatedly threatened to end the ceasefire.
The US had proposed an end to fighting before starting talks on more contentious issues, including Iran's nuclear program.
Tehran defended its stance on Monday.
"Our demand is legitimate," Foreign Ministry spokesperson Esmaeil Baghaei said.
Iran's parliament speaker Mohammad Baqer Qalibaf said Iran's armed forces are ready to respond decisively to any "act of aggression".
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.
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 voters facing higher gasoline prices less than six months before nationwide elections that will determine whether Trump's Republican Party retains control of Congress.
Two out of three Americans think Trump has not clearly explained why the country has gone to war, according to a Reuters/Ipsos poll completed on Monday.
The war is also exposing rifts within the Middle East, with some US allies taking a more direct role in the conflict. The United Arab Emirates, which has borne the brunt of Iranian counterattacks, has carried out military strikes on Iran, the Wall Street Journal reported on Monday, citing people familiar with the matter.
The strikes, which the UAE has not publicly acknowledged, included an attack on a refinery on Iran's Lavan Island in April, the Journal said. Reuters could not immediately verify the report.
At the time of the Friday strike on Lavan, the National Iranian Oil Refining and Distribution Company called it an "enemy attack". The next day, Iran's Mizan news agency reported it was carried out by Mirage fighter jets used by the UAE.
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 Tehran toward a deal with Washington.
