Iran's allies were celebrating on Wednesday after Washington withdrew the last of its forces from neighbouring Iraq, where 4500 US troops died in the biggest US war of the century.
More than 200,000 Iraqi civilians were killed in chaos unleashed after US forces toppled dictator Saddam Hussein in 2003.
Tehran views the pullout as a victory for its "axis of resistance" of allied armed groups, and a step towards its aim of driving US forces out of the region.
With the US-Israeli war against Iran now entering its eighth month, Iran put forward a proposal last week under which the United States would lift its blockade of Iranian ports and Iran would reopen the disrupted Strait of Hormuz within seven days.
Trump said on Sunday he had rejected the proposal, although Iranian Foreign Minister Abbas Araqchi said Tehran had not received a formal rejection.
In a post on X on Wednesday, an Iranian government spokesperson said Araqchi had conveyed a US response to the Iranian government.
Iran says its plan aims to restore an interim agreement that collapsed weeks after it was signed by Trump and Iran's President Masoud Pezeshkian in June.
Last week, Qatari mediators shuttled between US and Iranian envoys in New York on the sidelines of a meeting of the United Nations, the first proximity talks between the warring sides since the ceasefire unravelled.
An official briefed on the talks, who is not Iranian and spoke to Reuters on condition of anonymity, said the sides largely agree about the steps that are needed but still disagree about the order in which to take them.
Iran wants an eventual deal to grant it control over the Strait of Hormuz, the world's most important oil shipping route, which runs past its coast.
Shipping through the strait has increased in recent weeks, with shippers charging high fees to brave the risk of attacks.
But flows of crude oil, refined products and natural gas remain substantially disrupted.
US and Iraqi officials announced the withdrawal of the last American troops from bases in Iraq on Wednesday, fulfilling a plan agreed in 2024 under president Joe Biden and carried out by the Trump administration while it wages war with Iran next door.
The withdrawal was celebrated by Iran and its allies.
It marked an "historic victory for the Iraqi Islamic resistance groups and honourable Iraqis, and a crushing defeat for the American project", said Abu Mojtaba al-Yasiri, a commander in the Islamic Resistance in Iraq, an umbrella group of Iran-backed armed factions.
Iraq, which the United States invaded in 2003, has a Shi'ite majority like Iran, and Tehran has established broad political and military influence there.
The country has frequently become a proxy battlefield between the United States and Iran.
Of the 18 US service members listed as killed since Trump launched "Operation Epic Fury" in February, seven died in Iraq.
Washington blames Iran-backed groups in Iraq for striking neighbouring countries, most recently knocking out a big Saudi oil pipeline three weeks ago.
The US withdrawal raises "the possibility that Iran's proxies will feel increasingly empowered in the absence of a Western military presence", said Baghdad-based political analyst Ahmed Younis.
At home in the United States, polls show the Iran war was unpopular from the outset.
The disruption to global energy supplies and resulting surge in fuel prices have hurt Trump's Republicans, trying to hang on to both houses of Congress in legislative elections five weeks away.
In a letter to Americans, Iran's Islamic Revolutionary Guard Corps urged Americans on Tuesday to vote out Trump's allies.
"Make sure your politicians understand that the world has changed," they wrote.
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