He appeared to be reacting to a comment by Iran's foreign minister said Tehran would discuss its missile program after Washington stopped arming allies Saudi Arabia and the United Arab Emirates, something the United States is unlikely to do.
The surprising disclosures came hours after Iran's supreme leader upped the ante in the brewing confrontation by warning Tehran would continue removing restraints on its nuclear activity and retaliate for the seizure of an Iranian oil tanker.
Tensions have spiraled since Trump last year ditched big powers' 2015 nuclear deal with Iran under which it agreed to curtail its nuclear program in return for the lifting of global sanctions crippling its economy.
Washington has since reimposed draconian sanctions to throttle Iran's oil trade in a policy of "maximum pressure" on Tehran to agree stricter limits on its nuclear capacity, curb its ballistic missile program and end support for proxy forces in a Middle East power struggle with US-backed Gulf Arabs.
After threats from Ayatollah Ali Khamenei, Iran's ultimate authority, to push on with breaches of the nuclear deal, Trump suggested to a Cabinet meeting at the White House that Iran wanted to talk with its archenemy.
"A lot of progress has been made. We'll see what happens. But a lot of progress has been made," Trump said.
Trump said the Iran nuclear pact agreed under his predecessor Barack Obama was too weak to prevent Tehran developing atomic bombs. "They can't have a nuclear weapon. We want to help them. We'll be good to them, we'll work with them. We'll help them in any way we can, but they can't have a nuclear weapon. We're not looking, by the way, for regime change."
He added: "They (also) can't be testing ballistic missiles."
US Secretary State Mike Pompeo told the Cabinet meeting at the White House that Iran had signaled it was prepared to negotiate about its ballistic missiles.
"The Iranian regime is struggling to figure out what they're going to do with their economy because we've been terribly effective," Pompeo said.
"And the result is ... frankly, I think it was yesterday, maybe the day before, for the first time the Iranians have said that they're prepared to negotiate about their missile program. So we will have this opportunity, I hope, if we continue to execute our strategy appropriately, we'll have this opportunity to negotiate a deal that will actually prevent Iran from getting a nuclear weapon."
Pompeo appeared to be referring to comments by Iran's foreign minister on Monday in which he said Shi'ite Iran would discuss its missile program only after the United States ceased arming its regional Sunni rivals Saudi Arabia and the UAE.
Iranian Foreign Minister Mohammad Javad Zarif told NBC's "Nightly News with Lester Holt" program that once the Trump administration removed sanctions it has restored since leaving the nuclear deal the "room for negotiation is wide open."
Asked if that could include its ballistic missile program, Zarif replied: "If they want to talk about our missiles, they need, first, to stop selling all these weapons, including missiles, to our region."
There was no immediate comment from Tehran. The Islamic Republic has repeatedly ruled out negotiating under sanctions duress with Washington. It has long said its ballistic missile program is defensive in nature and non-negotiable.
Fears of direct US-Iranian conflict have risen since May with several attacks on oil tankers in the Gulf, Iran's downing of a US surveillance drone, and a plan for US air strikes on Iran last month that Trump called off at the last minute.
EU KEEN TO HEAD OFF WAR
In a strategy meeting on Monday, European parties to the nuclear deal decided on Monday not to trigger its dispute mechanism over Iran's breaches in favor of pursuing more troubleshooting diplomacy.
But they took no action to shield Iran against Trump's sanctions clampdown as Tehran has demanded in exchange for returning to full compliance with the 2015 deal.
Supreme leader Khamenei accused Britain, Germany and France of failing to uphold obligations under the deal to restore Iranian access to global trade, especially for Tehran's oil exports blocked by US sanctions.
"According to our foreign minister, Europe made 11 commitments, none of which they abided by. We abided by our commitments and even beyond them. Now that we've begun to reduce our commitments, they oppose it. How insolent! You didn't abide by your commitments!" Khamenei said, according to his website.
IMPASSE
He has previously upbraided European powers for not standing up to Trump and circumventing his sanctions noose. Russia and China are also parties to the accord.
But it was the first time Khamenei explicitly pledged to press ahead with breaches of the nuclear deal, spurning European appeals to Iran to restore limits on enrichment aimed at obviating any dash to development of atomic bombs.
"So far, efforts to win gestures from Iran to de-escalate the crisis are not succeeding (as) Tehran is demanding the lifting of sanctions on its oil and banking sectors first," a European diplomatic source told Reuters.
Iran denies any intent to acquire nuclear weapons, and has said all its breaches could be reversed if Washington returned to the deal and its economic dividends were realised. Tehran has accused Washington of waging "economic war."
"Western governments' major vice is their arrogance," Khamenei said. "If the country opposing them is a weak one, their arrogance works. But if it's a country that knows and stands up against them, they will be defeated."
IAEA inspectors last week confirmed Iran is now enriching uranium to 4.5pc fissile purity, above the 3.67pc limit set by its deal, the second breach in as many weeks after Tehran exceeded limits on its stock of low-enriched uranium.
The level at which Iran is now refining uranium is still well below the 20pc purity of enrichment Iran reached before the deal, and the 90pc needed to yield bomb-grade nuclear fuel. Low-enriched uranium provides fuel for civilian power plants.