Iran has reportedly suspended peace talks in protest over Israel’s deepening incursion into Lebanon, but US President Donald Trump insists progress is continuing.

Iran’s state media, closely tied to the Iranian Revolutionary Guard, reported on Tuesday (AEST) that Iran was suspending its participation in the negotiations.

The Iranian foreign minister, Abbas Araghchi, also stated that Israel’s ongoing attacks in Lebanon violated the ceasefire, making the US and Israel “responsible for the consequences of any violation”.

But as furious verbal barbs were fired from Iran, Trump insisted his critics should “just sit back and relax, it will all work out well in the end — It always ‌does!”.

Tensions between Israel and the Iran-aligned Hezbollah movement have escalated sharply in recent days.

Israeli forces have advanced deep into Lebanese territory, but remain far from the capital.

Both sides have carried out daily attacks, with casualties reported regularly, particularly in Lebanon.

Israeli Prime Minister Benjamin Netanyahu has threatened further strikes on Beirut’s southern suburbs.

However, Trump said he held a “very productive call” with Netanyahu and obtained agreement that there will be “no Troops going to Beirut, and any Troops that are on their way, have already been turned back.”

“Likewise, through highly placed Representatives, I had a very good call with Hezbollah, and they agreed that all shooting will stop — That Israel will not attack them, and they will not attack Israel.”

In a late-night social media post, Trump did not mention the exchange of hostilities, repeating his assertion that Iran “really wants to make a deal”.

Despite Trump’s ​remarks, Iranian Foreign Ministry spokesperson Esmaeil Baghaei accused Washington on Monday (local time) of constantly shifting its negotiating stance and condemned what he called US aggressive action.

He said sending contradictory messages would not work as a negotiating ​tactic, and urged ‌Washington to reach a clear and definitive position as soon as possible.

“Negotiations have started amid severe suspicion and mistrust, and the exchange of messages is taking place in this atmosphere,” Baghaei said.

“The other ​party is constantly changing its views and putting forward new or contradictory demands … it is natural that this situation will prolong negotiations,” he said, adding that Tehran viewed Israeli actions in the region, including in Lebanon, as inseparable from those of the US.

The ‌US and Iran have sporadically ⁠exchanged strikes since a ceasefire took effect in early April, while Pakistan has been mediating efforts to secure a more durable agreement. ​

The war launched by the US and Israel on February 28 has killed thousands of people, mainly in Iran and Lebanon. It has also caused global economic pain by pushing up energy prices since Iran effectively closed the Strait of Hormuz, a vital global supply route for oil and liquefied natural gas.

Trump is under pressure to reopen the Strait of Hormuz and get US petrol prices ​down ​before November congressional elections, as voters show increasing frustration over rising prices.

At the same ​time, he faces a potential backlash from Iran hawks in his own party over any concessions ‌to Tehran.

Trump has said his main aim in the war is to prevent Iran from developing a nuclear weapon with its highly enriched uranium. Tehran denies planning to develop a nuclear arsenal.

The two sides remain at odds on several issues, such as Tehran’s demands for the lifting of sanctions and the release of tens of billions of dollars of Iranian oil revenues frozen in foreign banks.

Israel’s war in Lebanon with the Iranian-backed Hezbollah militia is another impediment.

Netanyahu said on Sunday he had ordered troops to move further into Lebanon in the battle against Hezbollah.

Netanyahu on Monday ordered the military ​to attack targets in the Lebanese capital Beirut’s southern suburbs, a Hezbollah stronghold. His office accused Hezbollah of repeated violations of a ceasefire agreed in late April.

-with AAP