Iran and the US will hold a third round of nuclear talks on Thursday in Geneva, Oman's Foreign Minister Badr Albusaidi said on Sunday, amid growing concerns about the risk of military conflict between the longtime adversaries.

The US has built up its military presence in the Middle East, with President Donald Trump warning on Thursday that "really bad things will happen" if no deal is reached to solve a longstanding dispute over Tehran's nuclear programme.

"Pleased to confirm US-Iran negotiations are now set for Geneva this Thursday, with a positive push to go the extra mile towards finalizing the deal," said Oman's foreign minister, who acts as a mediator in indirect talks between Washington and Tehran.

Reuters reported on Sunday that Iran was offering fresh concessions on its nuclear programme in order to reach a deal, as long as it includes the lifting of economic sanctions and recognises Tehran's right to "peaceful nuclear enrichment".

Iran's President Masoud Pezeshkian voiced cautious optimism on Sunday in a post on X saying recent negotiations had "yielded encouraging signals", while pointing at Tehran's readiness for "any potential scenario".

Trump curious why Tehran hasn't 'capitulated'

Trump's special envoy Steve Witkoff, who leads nuclear negotiations on the US side, said on Saturday that the US president was curious as to why Iran has not yet "capitulated" and agreed to curb its nuclear programme.

"I don't want to use the word 'frustrated,' because he understands he has plenty of alternatives, but he's curious as to why they haven't... I don't want to use the word 'capitulated,' but why they haven't capitulated," Witkoff said during an interview with Fox News' "My View with Lara Trump," hosted by the president's daughter-in-law.

"Why, under this pressure, with the amount of seapower and naval power over there, why haven't they come to us and said, 'We profess we don't want a weapon, so here's what we're prepared to do'? And yet it's sort of hard to get them to that place."

Also Read: Tehran ready for nuclear concessions if US meets demands

Iran's Foreign Minister Abbas Araqchi reacted in a post on X saying: "Curious to know why we do not capitulate? Because we are Iranian."

He also said in an interview with CBS that a diplomatic solution with the US was still within reach.

Iran denies seeking nuclear weapons

Indirect talks last year did not bring any agreement, primarily due to friction over a US demand that Iran forgo uranium enrichment on its soil, which Washington views as a pathway to a nuclear bomb. Iran has denied seeking such weapons.

The US joined Israel in hitting Iranian nuclear sites in June, effectively curtailing Iran's uranium enrichment, with Trump saying its key nuclear sites were "obliterated". But Iran is still believed to possess stockpiles previously enriched, which Washington wants it to relinquish.

"They've been enriching well beyond the number that you need for civil nuclear. It's up to 60% (fissile purity)," Witkoff said. "They're probably a week away from having industrial, industrial-grade bomb-making material, and that's really dangerous."

Fresh concessions being considered by Iran include sending half of its highly enriched uranium abroad while diluting the rest.

Washington has also sought to expand the talks beyond the nuclear issue to cover Iran's missile programme and its support for regional armed groups. Iran has publicly rejected this, although sources have told Reuters that unlike the missiles, support for armed groups may not be a red line for Tehran.

Also Read: Iran hands sweeping powers to Larijani amid war preparations: US media

Another topic of friction is the scope and mechanism of lifting sanctions on Iran. A senior Iranian official told Reuters on Sunday that Iran and the United States still have differing views.

Witkoff also said he has met at Trump's direction with Iranian opposition figure Reza Pahlavi, son of the shah ousted in Iran's 1979 Islamic Revolution. He did not provide further details of the meeting.

Pahlavi, who lives in exile, served as a rallying figure for some of Iran's opposition during anti-government demonstrations last month in which thousands of people are believed to have been killed, the worst domestic unrest since the revolution era.

Earlier in February, Pahlavi said US military intervention in Iran could save lives, and urged Washington not to spend too long negotiating with Tehran's clerical rulers on a nuclear deal.