WASHINGTON/TEHRAN/LONDON – US President Donald Trump said on Monday that talks with Iran are "going on right now," adding that "this is a last chance," while Tehran said that an agreement with Oman on a new shipping route through the Strait of Hormuz was nearing completion.

"We're talking and we're talking at the request of Iran, backed by Saudi Arabia, backed by UAE and backed by Qatar in particular, but others also," Trump told reporters at the White House Oval Office after signing an executive order on military spouse.

"This is a last chance for them to sign a good document," Trump continued.

"I think we're going to maybe get something, but I want to give them every last chance before decapitation," he said.

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When asked about progress, Trump told reporters "you find out today or tomorrow ... they're going to go quickly one way or the other."

He said that the two sides are talking about the reopening of the Strait of Hormuz, "having it open literally by tomorrow, completely open, and that's phase one."

"And phase two is we then will talk about the nuclear capacity ... the denuclearization of Iran has to happen," he continued, adding that "that'll take a little while."

Earlier on the day, Trump took to social media to lash out at the Iranian leadership, accusing them of being "unbelievably duplicitous."

"They ask for a meeting, some would say 'beg,' talks begin, with more scheduled in the immediate future, and they say, openly and proudly, that they're not having any discussions, that nothing is being talked about, and they're only dealing with 'Oman,'" Trump wrote in a post on Truth Social.

Iranian Foreign Ministry spokesman Esmaeil Baghaei said in Tehran on Monday that Iran is currently not engaged in any negotiations with the United States, and talks with Oman over Strait of Hormuz are underway.

Earlier, Iranian officials rejected Trump's claim that Iran had asked the United States to cancel planned strikes.

Iranian President Masoud Pezeshkian said on Sunday that the existing framework agreement with the United States could provide a basis for future engagement with Washington.

ALSO READ: Trump says US to hold off attack on Iran

Many observers have questioned whether the latest diplomatic push will produce a lasting agreement.

Vali Nasr, an Iran expert at Johns Hopkins University, said there was "no clear path" for Trump to achieve his goals.

"He (Trump) is trying his hand now at a diplomatic solution to avoid military escalation. But there's no clear path, either diplomatically or militarily, to get Trump to a place where he can declare victory," said Nasr.

The announcement came with no reported phone call between Trump and Israeli Prime Minister Benjamin Netanyahu, who has been among the strongest advocates of maintaining pressure on Iran.

Israel has continued to stress that any agreement must prevent Iran from advancing its nuclear program and ballistic missile capabilities. Israeli Energy Minister Eli Cohen said that "with or without an agreement," Israel would take action if Iran sought to advance such efforts.

Hormuz route talks

Meanwhile, Iran and Oman have moved closer to an agreement on a new route through the Strait of Hormuz.

Iranian Foreign Minister Abbas Araghchi said negotiations with Oman on a mechanism for ships to transit the waterway were "nearing completion and in their final stages," according to Iranian state media.

Baghaei, the Iranian Foreign Ministry spokesperson, said Iran and Oman were working toward an understanding on a route acceptable to both parties, one that would respect sovereignty and safeguard national interests and security.

He stressed that the arrangement would not mean the immediate reopening of the Strait of Hormuz, where disputes over navigation arrangements remained unresolved.

The waterway has been at the center of the conflict, with Washington calling for free international navigation while Tehran has insisted on maintaining a role in managing passage through the strategic route.

Regional countries, including Oman, Qatar and Saudi Arabia, have continued efforts to reduce tensions and facilitate an agreement between Washington and Tehran.

UKMTO: Cargo vessel reports being hit by unknown projectile near Oman

In London, the United Kingdom Maritime Trade Operations said late Monday that a cargo vessel has reported that they have been hit by an unknown projectile off the coast of Oman.

According to a UKMTO advisory, the incident occurred earlier on Monday in waters about 20 nautical miles northeast of Al Khasab, Oman, near the eastern entrance to the Strait of Hormuz.

The UKMTO said it received a report from military authorities at 2200 GMT on Monday. The cargo vessel reported via VHF radio that it had been struck by an unknown projectile, the warning noted.

The UKMTO advised vessels transiting the area to exercise caution and report any suspicious activity to the agency.