The US and Iran held indirect talks over Tehran's nuclear programme on Thursday, but left the negotiating table without a deal.
They made "significant progress" in Geneva, Oman's Foreign Minister Badr al-Busaidi, who participated as a mediator, said afterwards, without elaborating.
It comes as the US has gathered a large fleet of aircraft and warships in the Middle East following widespread nationwide protests in Iran.
If the US launches an attack on Iran, Tehran has vowed to retaliate by targeting US military bases and by attacking Israel. On 19 February, Trump said that the world would find out "over the next, probably, 10 days" whether a deal would be reached or the US would take military action.
Talks to 'resume soon'
Donald Trump wants to reach a deal restricting Iran's nuclear programme and hopes to take advantage of the turmoil in Iran.
But Tehran appears to be standing firm, with state television reporting just before the talks ended that Iran was determined to continue enriching uranium - a key step to build a nuclear bomb - and had rejected proposals to transfer it abroad and sought the lifting of international sanctions.
Mediator Mr al-Busaidi said the talks "will resume soon", with technical-level negotiations to continue in Vienna next week.
The United Nations' atomic watchdog, the International Atomic Energy Agency, is based in Vienna and would likely be critical in any deal.
US Special Envoy Steve Witkoff, a billionaire real estate developer and friend of Mr Trump, led the US delegation at the talks, which also included the president's son-in-law, Jared Kushner.
Apart from demanding Iran halt its enrichment of uranium, which Tehran maintains it has the right to do, Mr Witkoff also tried to convince Iranian Foreign Minister Abbas Araghchi that Tehran should curtail or stop its production of long-range missiles, a topic Iran refused to discuss.
Iran says it will only discuss nuclear issues and claims its atomic programme is only for peaceful purposes.
Read more: Trump's plan for Iran isn't working - he has three options
'Most intense negotiations'
Mr Araghchi told Iranian state television that US-Iran talks were some of his country's "most intense and longest rounds of negotiations".
It was the third meeting since Israel launched a 12-day war against Iran last June, which saw the US carrying out strikes against several Iranian nuclear sites, leaving them in ruins.
Read more from Sky News:
Jerusalem braces for prospect of Middle East war
How Iran may be preparing for US strike
The Iranian delegation presented its latest proposal to its US counterparts and while Mr Araghchi offered no specifics on Tehran's demands, he said "what needs to happen has been clearly spelled out from our side".
The White House has not yet commented on Thursday's negotiations.
But Ali Vaez, an Iran expert for the International Crisis Group, told the Associated Press that it was a good sign that the US delegation did not walk away immediately after receiving Tehran's proposal, explaining that it shows "there is enough common ground between the two sides".
(c) Sky News 2026: 'Significant progress' in US-Iran talks - but no deal - as negotiations to resume next week
UFOs and Pizzagate: Hillary Clinton attacks line of questioning over Epstein
'I'm not the best father,' admits Volodymyr Zelenskyy as president says Ukraine hit by harshest winter for decades'
'Miracle' boy expected to be paralysed due to spina bifida able to walk after ground-breaking surgery in the womb
Child killer Ian Huntley will be vulnerable to another attack if he survives
Defence secretary orders search for record of Epstein trafficking women through RAF bases
Driver who crashed while gambling on mobile is jailed after pregnant woman suffered premature birth
Police apologise to second parliamentary Speaker in two days over Mandelson arrest leak
Assisted dying bill will almost certainly fail due to a lack of time