Speaking on the tarmac at Morristown airport before boarding Air Force One, Trump hailed "real progress, serious progress" following a fifth round of nuclear talks, which wrapped up in Rome on Friday.
The Oman-mediated talks, which began in April, are the highest-level contact between the countries since the United States quit a landmark 2015 nuclear accord during Trump's first term as US president.
Since returning to office, Trump has revived his "maximum pressure" campaign on Iran, backing talks but warning of military action if diplomacy fails.
Iran wants a new deal that would ease the sanctions that have battered its economy.
Following the latest round, Iranian Foreign Minister and lead negotiator Abbas Araghchi downplayed the progress, stressing that "the negotiations are too complicated to be resolved in two or three meetings."
And Omani Foreign Minister Badr Albusaidi said on X that the fifth round concluded "with some but not conclusive progress," adding that he hoped "the remaining issues" would be clarified in the coming days.
Trump said continuing discussions had been "very, very good."
"I think we could have some good news on the Iran front," he said, adding that an announcement could come "over the next two days."
The talks came ahead of a June meeting of the UN nuclear watchdog, the Vienna-based International Atomic Energy Agency (IAEA), during which Iran's nuclear activities will be reviewed.
They also come before the October expiry of the 2015 accord, which aimed to allay US and European Union suspicions that Iran was seeking nuclear weapons capability, an ambition that Tehran has consistently denied.
In return for curbs on its nuclear program, Iran had received relief from international sanctions. But the accord was torpedoed in 2018 when Trump unilaterally withdrew the United States and reimposed sanctions.
A year later, Iran responded by ramping up its nuclear activities.
It is now enriching uranium to 60 percent -- far above the deal's 3.67 percent cap but below the 90-percent level needed for a nuclear warhead.
bur-nl/aha
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