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.

Iran and the United States agreed on Monday to set up communications lines to keep the vital Strait of Hormuz open and end fighting in Lebanon, mediators said, after their first round of talks in Switzerland towards ending the war in the Middle East.

The teams led by US Vice President JD Vance and Iran's Mohammad Bagher Ghalibaf opened talks Sunday, starting a two-month negotiating period set out under a preliminary deal agreed last week.

Mediators Pakistan and Qatar said the talks took place in "a positive and constructive atmosphere".

"Encouraging progress has been made, including the creation of a mechanism for further technical talks," they said, detailing a contact channel set up to "avoid incidents and miscommunication" at the Strait of Hormuz".