The US president, Donald Trump, has said the peace deal with Iran is in its “final throes” and suggested that the strait of Hormuz could open up in “two or three days” if an agreement with Tehran is secured.

“It will open up immediately upon signing,” he told reporters on the tarmac at JFK airport, insisting that Iran will not be allowed nuclear weapons under the terms of a deal.

Trump said there are no “sticking points” that would prevent a deal from being reached, although the management of the strait, the way frozen Iranian assets are to be released and Israel’s war on Lebanon have all contributed to the deadlock in negotiations so far.

Trump has repeatedly threatened to resume full-scale bombing of Iran, although has pulled back several times as he likely knows that new strikes will keep the strait of Hormuz under the effective control of Iran and lead to an extremely dangerous escalation of attacks on US-allied Gulf states.

The effective closure of the strait has led to soaring energy prices around the globe, including in the US where the war is deeply unpopular. Trump said:

We are very close to having a very, very good strong, powerful deal. If we go and bomb – which we can do very easily if we want and we spend another two or three weeks bombing – they’ll have nothing left whatsoever but you won’t have the strait open for months.

If we do the bombing a lot of people are going to be killed. Who wants to do that? I don’t . And we’ll have a signed document that is actually stronger than doing the bombing.

Striking a rather casual tone, Trump told reporters Israel and Iran would leave each other alone for at least a week after he had a “very good conversation” with Israeli prime minister, Benjamin Netanyahu, who is under political pressure to continue his assault on Lebanon in order to degrade the military capabilities of Hezbollah, the Iranian-backed Lebanese militant group.

“He was hit, and he hit back, and I can’t blame him for that,” Trump said.

“But he was hit, he hit back, and now they’ve called it quits. So they’re going to just leave each other alone for another week or something.”

Israel, ignoring Trump’s wishes, attacked the southern suburbs of the Lebanese capital of Beirut on Sunday in what Tehran viewed as a violation of the US-Iran ceasefire. Israel claimed it was targeting Hezbollah infrastructure after it said the group fired rockets at northern Israel.

Iran in turn launched missiles at Israel on Sunday and a fresh exchange of fire between the two sides occurred yesterday. Iran announced a cessation of its fire after Trump demanded both sides stop “shooting” in a social media post.

Tehran said, however, that it would attack again if Israel persisted with its strikes in Lebanon, while Netanyahu warned that should Iran “make the mistake of resuming attacks against us, we will respond with full force”.