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In 2015, Iran and six world powers – the US, China, France, Russia, Germany and the UK – struck a deal allowing IAEA inspections of nuclear sites in Iran.
During Trump's first term, in 2018, he withdrew the US from this agreement, arguing it was a "bad deal".
Vance said on Monday that the Iranians had threatened to walk out of the talks on Sunday after Trump warned on Truth Social that the US could "hit Iran very hard again".
The US vice-president said he told Iranian negotiators that Trump was merely responding to Iranian "trash talk".
On Monday, Trump issued a fresh warning to Iran from the Oval Office.
"If Iran doesn't live up to their agreement, or if they're not behaving, I will do what I have to do," the US president said.
The Qatari and Pakistani mediators' joint statement said that a "communication line" had been formed "to avoid incidents and miscommunication with the aim of safe passage for commercial vessels through the Strait of Hormuz".
Both sides also agreed to the creation of a "de-confliction cell" between the US, Iran and Lebanon, facilitated by the mediating countries, to end military operations in Lebanon, their statement said.
Iran's Foreign Minister Seyed Abbas Araghchi said the first "real test" would be Lebanon.
Fighting between Israel and Hezbollah in Lebanon has abated since Saturday night and a fragile ceasefire was holding.
Negotiating groups are to be set up covering areas such as nuclear issues and sanctions as talks continue, Iranian state media reported on Tuesday.

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