Iran said on Monday that it still controls the Strait of Hormuz and is not seeking to resume talks with the United States, two days after President Donald Trump halted a bombing campaign that had run for 13 consecutive nights.

Foreign Ministry spokesperson Esmail Baghaei rejected suggestions Tehran had asked Washington for negotiations. "This is not in our DNA," he said.

Trump suspended the strikes on Saturday. Mike Waltz, the United States ambassador to the United Nations, said the pause was intended to allow room for negotiations. Trump's military advisers had told him that air defence munitions were running down and that the campaign had worked through its viable targets.

The dispute between the two governments is over a document they both signed. A framework agreed in June set the end of August as the deadline for talks. Washington reads its language on the Strait of Hormuz as requiring Iran to let ships pass freely. Tehran reads the same text as granting it the authority to supervise transit through the strait and to charge for it.

Iranian state media quoted an unnamed source as saying the traffic route through the strait is the one Iran specifies. Iran has said it turned back six vessels that tried to cross without its approval.

A senior Omani delegation was in Tehran over the weekend. Oman controls the southern shore of the strait, and Iran wants its supervision role written into an agreement with Muscat. Baghaei said those discussions went well.

Four United States service members were killed during the two-week campaign. Iran fired on American bases in the region while it was under way.

Brent crude fell about 6.5 per cent on Monday to just above US$90 a barrel, touching a low of US$87.55. It had passed US$100 last week for the first time since May.

Australia buys no crude from Iran but prices its fuel off international benchmarks. The federal government's 16 cent a litre fuel excise discount ends on 2 August.

The June framework set the end of August for talks to take place. Iran said on Monday it is not seeking them.