Days after the US floated an offer in the hopes of re-opening negotiations, Iran on Sunday released a response focused on ending the war on all fronts, especially Lebanon, where US ally Israel is fighting Iran-backed Hezbollah militants.
Tehran also included a demand for compensation for war damages and emphasised Iranian sovereignty over the Strait of Hormuz, Iranian state TV said.
It also called on the US to end its naval blockade, guarantee no further attacks, lift sanctions and end a US ban on Iranian oil sales, the semi-official Tasnim news agency said.
Within hours, Trump dismissed Iran's proposal with a post on social media.
"I don't like it — TOTALLY UNACCEPTABLE," Trump wrote on Truth Social, without giving further detail.
The US had proposed an end to fighting before starting talks on more contentious issues, including Iran's nuclear program.
Oil prices jumped $US3 ($A4.1) a barrel on Monday following news of the continued stalemate that leaves the narrow Strait of Hormuz largely closed.
Before the war the waterway carried one-fifth of the world's oil supply and has emerged as one of the central pressure points in the war.
Surveys show the war is unpopular with US voters facing sharply higher gasoline prices less than six months before nationwide elections that will determine whether Trump's Republican party retains control of Congress.
The US has also found little international support, with NATO allies refusing calls to send ships to open the Strait of Hormuz without a full peace deal and an internationally mandated mission.
It's not clear what fresh diplomatic or military steps may be ahead.
Trump is expected to arrive in Beijing on Wednesday. With mounting pressure to draw a line under the war and the global energy crisis it has ignited, Iran is among topics Trump and Chinese President Xi Jinping are set to discuss.
Trump has been leaning on China to use its influence to push Tehran to make a deal with Washington.
Addressing whether combat operations against Iran were over, Trump said in remarks aired on Sunday: "They are defeated, but that doesn't mean they're done."
Israeli Prime Minister Benjamin Netanyahu said the war was not over because there was "more work to be done" to remove enriched uranium from Iran, dismantle enrichment sites and address Iran's proxies and ballistic missile capabilities.
The best way to remove the enriched uranium would be through diplomacy, Netanyahu said in an interview that aired Sunday on CBS News' "60 Minutes." But he did not rule out removing it by force.
Iran's President Masoud Pezeshkian said in a social media post that Iran would "never bow down to the enemy" and would "defend national interests with strength".
Despite diplomatic efforts to break a deadlock, the threat to shipping lanes and the economies of the region remained high. Recent days have seen the biggest flare-ups in fighting in and around the strait since a ceasefire began.
On Sunday, the United Arab Emirates said it intercepted two drones coming from Iran, while Qatar condemned a drone attack that hit a cargo ship coming from Abu Dhabi in its waters. Kuwait said its air defences had dealt with hostile drones that entered its airspace.
Clashes have also continued in southern Lebanon between Israel and Iran-backed militant group Hezbollah, despite a US-brokered ceasefire announced on April 16.
An end to hostilities with Iran would not necessarily bring an end to the war in Lebanon, Netanyahu said in the 60 Minutes interview, in which he also said Israeli planners had underestimated Iran's ability to choke off traffic through the Hormuz Strait.
"It took a while for them to understand how big that risk is, which they understand now," he said.
