Badr al-Busaidi wrote on X that there had been "significant progress in the negotiation," without elaborating. He said technical-level talks would take place next week in Vienna, home to the International Atomic Energy Agency.
He earlier said said the two sides have been exchanging "creative and positive ideas".
There was no immediate comment from US or Iranian officials.
Analysts had been concerned that ending the talks without an immediate deal could spark US military action against Iran.
US President Donald Trump wants a deal to constrain Iran's nuclear program, and he sees an opportunity while the country is struggling at home with growing dissent following nationwide protests in January.
Iran, meanwhile, has maintained it wants to continue to enrich uranium even as its program sits in ruins, following Trump ordering an attack in June on three of the Islamic Republic's nuclear sites, part of a bruising 12-day war in 2025.
If an American attack happens, Iran has said all US military bases in the Middle East would be considered legitimate targets, putting at risk tens of thousands of American service members.
Iran has also threatened to attack Israel, meaning a regional war again could erupt across the Middle East.
"There would be no victory for anybody - it would be a devastating war," Iranian Foreign Minister Abbas Araghchi told India Today in an interview filmed just before he flew to Geneva.
In Washington Democratic leaders say they will force a vote next week on legislation requiring President Trump to terminate military force against Iran unless explicitly authorised by a declaration of war from Congress.
Democratic leader Hakeem Jeffries was joined in the announcement by several Democrats who serve as the ranking member on committees with jurisdiction.
Their press release on Thursday said the Iranian government is "brutal and destabilising," and cited the killing of thousands of protesters.
"However, undertaking a war of choice in the Middle East, without a full understanding of all the attendant risks to our servicemembers and to escalation, is reckless," the release stated. "We maintain that any such action would be unconstitutional without consultation with and authorisation from Congress."
Oman is mediating between Araghchi and Steve Witkoff, a billionaire real estate developer and friend of Trump who serves as a special Mideast envoy for the president.
The two men held rounds of talks in 2025 that collapsed after Israel launched its war against Iran in June. On Thursday Oman later published images of Witkoff and Jared Kushner, Trump's son-in-law, meeting al-Busaidi at the residence, as well as images of al-Busaidi meeting Araghchi, signalling the start of the talks.
In this round of negotiations after the June war, Trump has pushed to halt Iran's enrichment of uranium entirely, as well as address Tehran's ballistic missile program and its support of regional militant forces.
Iran maintains the talks must remain focused only on nuclear issues.
US Secretary of State Marco Rubio told reporters on Wednesday that Iran was "always trying to rebuild elements" of its nuclear program.
He said Tehran was not enriching uranium right now, "but they're trying to get to the point where they ultimately can".
Iran has said it has not enriched since June, but it has blocked International Atomic Energy Agency inspectors from visiting the sites America bombed.
The West and the IAEA say Iran had a nuclear weapons program until 2003.
Before the June attack, it had been enriching uranium up to 60 per cent purity - a short, technical step away from weapons-grade levels of 90 per cent.
US intelligence agencies assess that Iran has yet to restart a weapons program, but has "undertaken activities that better position it to produce a nuclear device, if it chooses to do so".
While insisting its program is peaceful, Iranian officials have threatened to pursue the bomb in recent years.
