US President Donald Trump has said discussions involving Iran are progressing well, but renewed his threat of major military action if Tehran does not agree to reopen the Strait of Hormuz.

“We are having very good discussions,” Trump told Fox News after what he described as a day-long negotiation on Tuesday.

Trump said the strategic waterway would reopen “very soon” and warned: “If they back out again, they are going to get hit really hard.”

Speaking separately before leaving California for Nevada, the president said he believed an agreement could be reached on Wednesday or Thursday.

“We hit them very, very hard. But the hard hit is yet to come, and hopefully we won’t have to use it,” Trump said.

Iran has publicly denied holding direct negotiations with the United States. Tehran says it is discussing safe shipping arrangements with Oman, which shares the strait, while Washington and several regional governments participate through diplomatic channels.

Iranian Foreign Ministry spokesman Esmaeil Baghaei said the talks with Oman were positive and continuing. He said the proposed routes must protect the sovereignty and national security of both coastal states.

Axios reported that the United States, Iran and Oman were close to an interim agreement, citing two regional sources and a US official. Washington was seeking to announce the deal on Wednesday, but none of the three governments had formally confirmed that it had been finalised.

The proposed arrangement would remain in place for 60 days and could be extended.

Under the draft, ships entering the Gulf would use a northern lane through Iranian territorial waters. Vessels leaving the Gulf would travel through a southern lane in Omani waters, with coordination between Muscat and Tehran.

No tolls or service charges would be collected during the temporary arrangement.

The proposal would also require naval mines to be cleared from the central section of the strait within 30 days. That route could later accommodate traffic in both directions under a permanent agreement negotiated by Iran and Oman.

Axios reported that US envoy Steve Witkoff had spoken with Iranian Foreign Minister Abbas Araghchi and his Omani counterpart Badr al-Busaidi during the negotiations. Qatar, Pakistan and Saudi Arabia have also participated in mediation efforts.

Iranian state media, however, cited an informed source as saying that an agreement with Oman would be delayed for as long as the United States continued to threaten Iran.

The differing accounts highlight the uncertainty surrounding the negotiations. Trump portrays the discussions as direct engagement with Tehran, while Iranian officials describe them as talks with Oman about navigation and maritime security.

The emerging agreement is intended to restore commercial traffic and create conditions for broader negotiations aimed at ending the five-month conflict and addressing Iran’s nuclear programme.

Trump suspended a planned wave of US strikes over the weekend to allow more time for diplomacy. He has described the current negotiations as Iran’s final opportunity to avoid a further escalation.

The Strait of Hormuz normally carries about one-fifth of global oil and liquefied natural gas shipments. Most traffic through the waterway has been halted since the conflict began in February.

Oil prices extended their decline and global shares rose on Wednesday as investors reacted to reports that an agreement could be close.

The International Maritime Organization had recorded 64 confirmed maritime incidents in the region by 4 August, resulting in the deaths of at least 17 seafarers.