Iran hours earlier had temporarily reopened the Strait of Hormuz following a separate US-brokered ceasefire agreement by Israel and Lebanon.
But subsequent statements from both sides left uncertainty over how quickly shipping might return to normal through the global oil choke point.
Trump, speaking on Air Force One late on Friday, declined to elaborate on what the good news was.
"It seems to be going very well in the Middle East with Iran," he told reporters while returning to Washington from Phoenix, Arizona.
"We're negotiating over the weekend. I expect things to go well. Many of these things have been negotiated and agreed to.
"The main thing is that Iran will not have a nuclear weapon. You cannot let Iran have a nuclear weapon, and that supersedes everything else."
But in sharp contrast, he said he may end the ceasefire with Iran unless a long-term deal to end the war is agreed before it expires on Wednesday, adding a US blockade of Iranian ports would continue.
The war with Iran, which began on February 28 with a US-Israeli attack, has killed thousands and sent oil prices surging because of the de facto closure of the strait, which until recently carried about a fifth of the world's oil trade.
Trump has told Reuters there would probably be more direct talks between Iran and the US this weekend. Some diplomats said that was unlikely given the logistics of gathering in Islamabad, where the talks are expected to take place.
There were no signs of preparations early on Saturday for talks in the Pakistani capital, where the highest-level US-Iran negotiations since the 1979 Islamic Revolution ended without agreement last weekend.
The key Pakistani mediator, army chief Field Marshal Asim Munir, has been holding talks in Tehran since Wednesday.
A Pakistani source aware of mediation efforts said a meeting between Iran and the US could produce an initial memorandum of understanding, followed by a comprehensive peace agreement within 60 days.
Among complicating factors, Iran's speaker of parliament and senior negotiator, Mohammad Baqer Qalibaf, posted on social media that the Strait of Hormuz "will not remain open" if the US blockade continued.
Foreign Minister Abbas Araqchi had announced on social media that the strait was open for all commercial vessels for the remainder of the 10-day truce that was agreed on Thursday by Israel and Lebanon, which was invaded by Israel after the Iran-allied Hezbollah militant group joined the fighting.
Vessel traffic data showed a group of around 20 ships, including container ships, bulk carriers and tankers, moving through the Gulf toward the Strait of Hormuz on Friday evening, but most ended up turning back, although it was not clear why.
Iran has said all ships crossing the strait must co-ordinate with the Islamic Revolutionary Guard Corps, which was not the case before the war.
The Defense Ministry said in a statement quoted by state television that military vessels and ships linked to "hostile forces" - the US and Israel - were still not permitted to pass.
Shipping companies have said they would require clarifications, including about the risk of mines, before vessels moved through the entry point to the Gulf.
The US Navy warned seafarers the mine threat in parts of the waterway was not fully understood and said they should consider avoiding the area.
It also was unclear how Iran and the US would address Tehran's nuclear program, which has been a key sticking point in peace talks, with Iran defending its right to what it says is a civilian nuclear energy program.
Trump told Reuters the US would remove Iran's stockpiles of enriched uranium. Foreign Ministry spokesperson Esmaeil Baghaei told state TV the material would not be transferred anywhere.
Oil prices fell about 10 per cent and global stocks jumped on Friday on the prospect of marine traffic resuming through the strait.
After a video conference on Friday, more than a dozen countries said they were willing to join an international mission to protect shipping in the strait when conditions permit, Britain said.
A senior Iranian official told Reuters there had been an agreement on unfreezing billions of dollars in Iranian assets as part of the accord, without giving a timeline.
Later on Friday, Trump, who has repeatedly referred to a peace agreement as a "deal" or "transaction", told a rally in Arizona that "no money will exchange hands in any way, shape or form."
