Qatar has floated a new plan to restore shipping through the Strait of Hormuz and end the conflict between the United States and Iran, despite reports of renewed US strikes on a key Iranian island.

Sheikh Tamim bin Hamad al-Thani, the emir of mediating Qatar, spoke with US president Donald Trump about their vision for a deal to end the eight-month war, Qatari media reported on Friday.

Al-Thani said on Saturday that the Trump administration was willing to find a solution after the midterm elections, which produced a damning verdict of the conflict and its impact on fuel prices last week.

Under Qatar’s proposal, the US would lift its blockade on Iranian ports and release some of its £6bn worth of frozen Iranian assets, according to the Guardian.

Iran would also agree to visits by IAEA nuclear watchdog inspectors to its main facilities, before reopening the Strait of Hormuz to commercial traffic on the second day, the newspaper said.

Under the Qatari deal, and crucially for Trump, who casus belli was that Iran should never be able to acquire nuclear weapons, the regime would apparently not have to give up its nuclear stockpiles.

The Islamic Republic has made overtures to controlling the vital Strait, through which around a fifth of global oil normally passes, with Oman after the war and could begin charging fees for safe passage.

Under the Qatari deal, Tehran would reopen the route already agreed with Muscat, to be jointly lodged with the International Maritime Organisation (IMO).

Oman’s foreign minister, Badr Albusaidi, has separately spoken with Iran about the future administration of the Strait, including the need to register the proposal with the IMO.

Muscat has its own long-term proposal for the running of the channel, which would only see shipping companies charged for services, not tolls per se.

Iran has also sought to resolve a number of secondary issues thrown by the conflict, which began with US-Israeli strikes on February 28.

Ending the parallel clashes in Lebanon, pulling US forces back from the region and paying war reparations are all new obstacles that will require mediation.

Tehran has been proposing its own seven-day plan to end the war since September, but that has so far been rejected by Trump.

It calls for Washington to lift its blockade, unfreeze assets and approve an Iranian-backed route through the Strait of Hormuz, after which the contested waterway would be reopened.

A senior Iranian official told Reuters on Thursday that Tehran has also submitted a nuclear proposal to Washington through Qatar.

They said the US was reviewing its but that future discussions would still depend on Washington first meeting Tehran’s seven stated demands.

Ali Bagheri Kani, the deputy head of Iran’s top security body, told Iranian state television on Friday that they were still not satisfied with “paper commitments” and must see practical steps from the US.

With diplomatic efforts still on ice, Iranian media on Saturday said it appeared two missiles had struck Qeshm Island in the Strait of Hormuz.

Iran has repeatedly said it would respond to new attacks by striking at US and Israeli targets in neighboring countries.

The United States has not yet announced any attack on targets inside Iran.