Cracks began to appear last night in the terms of the Iran peace deal – with disputes centring on the status of Lebanon and free passage through the Strait of Hormuz.

Only a day after the US announced a breakthrough agreement with Iran to end more than three months of conflict, Israel said yesterday its forces would not withdraw from southern Lebanon, saying the deal between Washington and Tehran 'does not bind us in any way'.

Lebanon has been a key sticking point in the negotiations, with Israel and Iran-backed Hezbollah still exchanging fire despite US calls for a ceasefire.

While Hezbollah welcomed the US-Iran memorandum of understanding – expected to be signed on Friday – Benjamin Netanyahu insisted Israeli troops would remain in Lebanon 'as long as necessary'.

In a press conference yesterday, the Israeli prime minister said his country would maintain the freedom of action needed to thwart attacks coming from Lebanon: 'We have created a buffer zone, a security zone. We'll remain there as long as necessary. I stood firm on this point. I was truly adamant about this and I think our American friends respected this.'

A US official also said Israel's withdrawal from Lebanon was excluded from any deal between the US and Iran, adding: 'The deal is a ceasefire, and it will not be a one-way ceasefire, meaning if Iran is not able to control Hezbollah, and if they attack Israeli positions or towns, Israel will have the right to defend itself and respond.'

But Iran's foreign minister, Abbas Araghchi, in a call with the Lebanese president Joseph Aoun, said that Lebanon's 'sovereignty' must be respected.

Mr Netanyahu also said he did not always 'see eye to eye' with Donald Trump a day after reports emerged that the US President slapped down his Israeli counterpart during an expletive-laden phone call over strikes on Beirut. 

The Israeli PM added that his country had been saved from the danger of 'nuclear destruction' by starting a joint war with the US on Iran, which he declared would not have a nuclear weapon.

'Our struggle has not yet ended,' he said. Israel's national security minister Itamar Ben-Gvir dismissed the deal, saying it failed to guarantee Israel's security and 'does not bind us in any way'.

Mr Ben-Gvir said Israel should not settle for anything less than 'the dismantling of Hezbollah', urging continued action against the group. Defence minister Israel Katz indicated his country would resist pressure to withdraw from areas held in southern Lebanon.

Pakistan, acting as mediator, said the deal included the 'immediate and permanent termination of military operations on all fronts, including in Lebanon'.

Ships have already started to pass through the Strait of Hormuz again as Mr Trump said the crucial route would reopen under the deal with Tehran. 

But conflicting reports have emerged from the US and Iran over whether ships will be forced to pay to use the world's key energy corridor.

Iranian sources have signalled that Tehran intends to introduce charges on ships in the strait in what would appear to be a major concession by the President. 

But it directly contradicts Mr Trump's earlier claim that the route would be 'permanently toll-free'. Vice-President JD Vance insisted last night that the US expected the strait to remain free, claiming the US held 'all the cards' in talks.

'Our expectation is that the strait is going to be opened in a toll-free way for the long term,' he said, adding that 'a lot' of the details remained to be hammered out in technical negotiations.

Hormuz, a passage for a fifth of the world's oil and gas supply, has been effectively closed since US-Israeli strikes on Iran in February rocked energy markets.

After saying it would reopen on Friday, Mr Trump appeared to declare it open for business yesterday on social media. He said ships 'many loaded up with oil' were starting to pass through the strait's southern shipping lane.

The deal came after reports of 11th-hour concessions to get the agreement over the line on Sunday – Mr Trump's 80th birthday.

Those changes were said to have followed Israeli strikes on Beirut that morning, which breached a ceasefire and drew anger from both Tehran and Washington.