US President Donald Trump said Monday that talks with Iran were moving at a "rapid pace", even as Tehran threatened to widen the war by keeping the Strait of Hormuz blocked and activating other pressure points around the region.

Iran's Tasnim news agency reported that Tehran had suspended dialogue with mediators over Israel's expanding offensive in Lebanon, where the US ally again threatened strikes on Beirut's southern suburbs.

Trump later said he had persuaded Israel and Iran-backed Hezbollah to de-escalate, with Lebanon's US embassy saying the militant group had accepted a US proposal for a "mutual cessation of attacks".