Iranian Foreign Minister Abbas Araqchi posted on his Telegram channel that his delegation had a brief encounter with its US counterpart, headed by Trump's Middle East envoy Steve Witkoff, after they exited the indirect talks mediated by Oman.
"After the end of more than two and a half hours of indirect talks, the heads of the Iranian and American delegations spoke for a few minutes in the presence of the Omani foreign minister as they left the talks," Araqchi said.
He said the talks took place in a "productive and positive atmosphere".
"Both sides have agreed to continue the talks next week," Araqchi wrote, without elaborating about the venue and date.
There was no immediate US comment on the talks.
Underlining the profound rift between the US and Iran, Iranian Foreign Ministry spokesman Esmail Baghaei earlier said on X that each delegation had its separate room and would exchange messages via Oman's foreign minister.
"The current focus of the talks will be de-escalating regional tensions, prisoner exchanges and limited agreements to ease sanctions (against Iran) in exchange for controlling Iran's nuclear program," an Omani source told Reuters.
Baghaei denied this account but did not specify what was false.
Aragachi later told Iranian state TV that the next round of talks will take place on April 19.
He described the negotiations so far as constructive, telling state TV there were four rounds of messages exchanged indirectly between Iran and the US during the talks in Muscat.
The talks began about 330pm local time on Saturday.
The two sides spoke for more than two hours, ending the talks about 5.50pm.
The convoy believed to be carrying Witkoff returned to Muscat, the capital of Oman, before disappearing into traffic around a neighbourhood that is home to the US embassy.
Omani Foreign Minister Badr al-Busaidi said on X the talks had taken place "in a friendly atmosphere conducive to bridging viewpoints".
While the US side can offer sanctions relief for the beleaguered Iranian economy, it remains unclear just how much Iranian officials will be willing to concede.
Under a 2015 nuclear deal, Iran could only maintain a small stockpile of uranium enriched to 3.67 per cent.
Today, Iran's stockpile could allow it to build multiple nuclear weapons if it so chooses and it has some material enriched up to 60 per cent, a short technical step away from weapons-grade levels.
Judging from negotiations since Trump unilaterally withdrew the US from the deal in 2018, Iran will likely ask to keep enriching uranium up to at least 20 per cent.
Signs of progress could help cool tensions in a region aflame since 2023 with wars in the Gaza Strip and Lebanon, missile fire between Iran and Israel, Houthi attacks on Red Sea shipping and the overthrow of the government in Syria.
with AP