Meanwhile, Washington is gripped by a legalistic debate over whether Trump has passed a deadline for requesting congressional approval for the war.
US President Donald Trump said on Friday that he is "not satisfied" with a new Iranian negotiating proposal, with peace talks between the two sides frozen despite a weeks-long ceasefire.
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Iran delivered the text of the proposal to mediator Pakistan on Thursday evening, the IRNA news agency reported, without offering details about its contents.
"At this moment I'm not satisfied with what they're offering," Trump told reporters, laying blame for the stalled talks with Iran due to "tremendous discord" within its leadership.
"Do we want to go and just blast the hell out of them and finish them forever or do we want to try and make a deal? I mean, those are the options," he said when asked about next steps, adding he would "prefer not" to take the first option "on a human basis."
The war, launched by the United States and Israel with a wave of surprise strikes on 28 February, has been on hold since 8 April, but only one failed round of direct talks has taken place between Iranian and US representatives.
In the meantime, Iran has maintained its stranglehold on the Strait of Hormuz, cutting off vast amounts of oil, gas and fertiliser from the world economy, while the US has imposed a counterblockade on Iranian ports.
Despite the failure to negotiate an end to the war, the ceasefire has held. On Friday, judiciary chief Gholamhossein Mohseni Ejei said "the Islamic Republic has never shied away from negotiations."
But he added in a video shared by the judiciary's Mizan Online website, "we certainly do not accept imposition," though Tehran did not want a return to war.
Scant details
The White House has declined to comment on the details of the new Iranian proposal.
But the news site Axios reported that US envoy Steve Witkoff earlier this week had submitted amendments to a previous proposal seeking to reinject the issue of Tehran's nuclear programme into the negotiations.
Citing a source familiar with the matter, Axios said they included a demand that Iran not try to move enriched uranium out of sites bombed during a brief war last year, or resume any activity there while talks continue.
Optimism after news of the Iranian proposal sent oil prices falling by nearly 5% for US benchmark West Texas Intermediate.
However, prices are still roughly 50% above their pre-war levels as traders confront the prolonged closure of Hormuz.
An EU official said that the bloc's foreign policy chief Kaja Kallas had spoken with Iran's foreign minister Abbas Araghchi by phone on Friday about diplomatic efforts to reopen the strait.
War powers debate
Meanwhile, Washington is gripped by a legalistic debate over whether Trump had passed a deadline for requesting congressional approval for his war with Iran.
Administration officials have insisted that the ceasefire means the clock is paused on a 60-day deadline requiring the president to seek war powers authorisation from Congress.
Trump echoed that rationale on Friday, insisting the United States was "in the midst of a big victory."
Trump is under increasing domestic pressure over the war, with inflation spiking, no clear victory in sight and mid-term elections due in November.
In Iran, meanwhile, the economic consequences of the war, which come on top of years of fierce international sanctions, were beginning to bite.
The US imposed new sanctions on three Iranian foreign currency exchange firms on Friday, while the Treasury warned others that paying a "toll" to Tehran for safe passage through the Strait of Hormuz could trigger sanctions as well.
On Thursday, the US military said its blockade had stopped Iran from exporting $6 billion (€5.1 billion) worth of oil, while inflation has risen past 50% in recent weeks.