Tehran, Iran - Iran's delegation on Sunday walked out of the Swiss venue where it held talks with the US towards permanently ending the Middle East war, after Donald Trump threatened to strike the Islamic Republic over its support for Hezbollah.

The negotiations to end a war that sowed chaos across the region and rattled the global economy are meant to trigger a 60-day period to settle broader issues that have dogged US-Iranian relations for decades.

But disagreement over key sticking points and the threat of renewed fighting in Lebanon weighed on the talks, with Washington and Tehran exchanging threats in parallel with the negotiations.

"The delegation of the Islamic Republic of Iran, after meeting with the Qatari delegation as one of the mediating parties, left the building where the negotiations were being held," Iran's state news agency IRNA said.

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"At the same time as the talks began in Switzerland, Donald Trump published a message on X in which he repeated his threats and remarks against Iran," it added.

A diplomat with knowledge of the talks, however, told AFP that the Iranians had not quit the negotiations.

"The Iranian delegation remains engaged in the talks and has not indicated to the mediators any intention to leave," the diplomat said on condition of anonymity.

Trump had earlier threatened to strike Iran if it did not "immediately stop their highly paid PROXIES in Lebanon from causing trouble".

Iran hit back with a warning of its own.

"They would do better to be careful with their statements; our armed forces are ready to respond to them in a different manner. No matter what they say, we are the ones who act," Iran's chief negotiator Mohammad Bagher Ghalibaf said.