TEHRAN : 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".

"Talks are continuing, at a rapid pace, with the Islamic Republic of Iran," Trump posted on social media.

Weeks of indirect US-Iran talks, threats and air strikes have failed to end the war or reopen the Strait of Hormuz, the key shipping channel for Gulf oil and gas.

The latest overnight US-Iran exchange of fire coincided with Israel expanding its ground offensive in Lebanon, where Prime Minister Benjamin Netanyahu vowed to push deeper and threatened strikes on "terror targets" in Beirut's southern suburbs.

Israel's Arabic-language spokesman told residents of the suburbs, known as Dahiyeh, to evacuate "to preserve their safety", and AFP images showed huge traffic jams as people fled.

Netanyahu later said he had told Trump that Israel would strike Beirut if Hezbollah did not stop attacking Israel, while continuing operations in southern Lebanon.

The United States has backed Israel's operations against Hezbollah, while pursuing a deal with Iran to end the war, reopen Hormuz and impose controls on Iran's nuclear programme.

But Iran again said Monday it had not entered nuclear negotiations and insisted Israel must halt its Lebanon offensive before any wider deal could be agreed.

Ahead of a Security Council emergency meeting on Lebanon, UN chief Antonio Guterres's spokesman said: "We are deeply alarmed by the escalation in military activities across southern Lebanon and beyond."

- 'Direct war' -

Iran's chief negotiator Mohammad Bagher Ghalibaf said the US naval blockade and Lebanon escalation were "clear evidence of US non-compliance with the ceasefire".

Late Monday, Tasnim reported that Iran was suspending "dialogues and exchange of texts through mediators" over Israel's actions in Lebanon.

In a message carried by state TV, the Revolutionary Guards intelligence body said "crossing the red lines in Lebanon and Gaza" would mean "direct war".

It said Iran was determined to preserve what it called the "Strait of Hormuz equation" and to take "meaningful actions" by opening other fronts.

Trump told NBC that did not mean Washington would "start dropping bombs all over there", but insisted the US naval blockade would remain.

Tasnim reported that Iran would keep Hormuz blocked and, with its allies, "activate other fronts", including the Bab al-Mandab Strait at the entrance of the Red Sea.

Tehran's Houthi allies in Yemen have previously attacked shipping near Bab al-Mandab, whose closure could disrupt millions more barrels of oil exported daily by Saudi Arabia through its Red Sea port of Yanbu.

In another sign of danger to Gulf shipping, the UKMTO maritime agency reported a "large explosion" on a cargo vessel off Iraq "following a hit from an unknown projectile".

- Nuclear impasse -

Iranian foreign ministry spokesman Esmaeil Baqaei said: "No negotiations have taken place on the details of the nuclear file. At this stage, our priority is ending the war."

Trump insists Iran's nuclear programme must be part of any deal, saying Tehran must not get nuclear weapons -- ambitions Iran denies.

"We insist that a ceasefire in Lebanon is an essential condition for any deal aimed at ending the war," Baqaei said, adding that the United States was also violating the ceasefire.

The US military said it carried out "self-defense strikes" on Iranian radar and drone control sites over the weekend -- its third such wave in just over a week -- after a US MQ-1 drone was downed.

The Revolutionary Guards later told state media they had targeted an airbase used by the US military for the attack.

They did not identify the country hosting the base, but Kuwait's military said its air defences intercepted "hostile missile and drone attacks".

The Israeli army also announced that two more soldiers had been killed in southern Lebanon, bringing Israeli military deaths since early March to 27.