Days after the US floated an offer in the hopes of reopening 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 damage 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, posting on Truth Social: "I don't like it - TOTALLY UNACCEPTABLE," without giving further detail.
The US had proposed an end to fighting before starting talks on more contentious issues, including Iran's nuclear program.
Following Trump's rejection of its demands, Tehran said on Monday it believed its proposal to end the war was "generous and responsible".
"Our demand is legitimate: demanding an end to the war, lifting the (US) blockade and piracy, and releasing Iranian assets that have been unjustly frozen in banks due to US 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 for regional security."
Oil prices jumped by more than 3.5 per cent on Monday on news of the continued deadlock that leaves 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 flows, and has emerged as one of the central pressure points in the war.
While traffic through the Strait of Hormuz is at a trickle compared with before the war, shipping data on Kpler and LSEG showed three tankers laden with crude exited the waterway last week, with trackers switched off to avoid Iranian attack.
Sporadic flare-ups in fighting around the strait in recent days have tested a ceasefire that has paused all-out warfare since it took effect in early April.
Surveys show the war is unpopular with US voters facing sharply higher petrol 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 is not clear what fresh diplomatic or military steps might be ahead.
Trump is expected to arrive in Beijing on Wednesday, and Iran is among the 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 aired Sunday on CBS News' 60 Minutes, but he did not rule out removing it by force.
Iranian 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".
