Donald Trump has again threatened to bomb Oman if it "gets in the way" of his effort to end the US-Israel war on Iran, as the two-month window to negotiate peace with Iran expired on Monday with no end to the conflict in sight.

The latest threats against Oman, which is not a party to the war, have illustrated how Trump's unpredictable and often outrageous approach to diplomacy has upset US partners and failed to achieve the breakthrough that he has promised to end the war.

"If Oman gets in the way, we'll bomb the shit out of them," Trump told Fox News on Monday, the second time he has directed such a threat at Muscat, a longtime US strategic partner that has traditionally served as a key backchannel between Washington and Tehran.

The various conflicts in the Middle East continued on Monday, with Yemen's Houthis claiming to have targeted military ships from Saudi Arabia – a US ally – in a missile and drone strike in the Red Sea. Saudi officials did not confirm the strike, which the Houthis said had struck a Saudi military ship and four escort vessels. The attack is said to have taken place at a port close to the Bab-al Mandeb strait, an important global shipping route that connects the Red Sea to the Gulf of Aden.

In Israel, Trump's son-in-law Jared Kushner met Benjamin Netanyahu for more than four hours after the Israeli prime minister rejected a US-backed peace plan for the Gaza war that included a withdrawal of Israeli troops from the devastated territory. Netanyahu has said he rejected any withdrawal that would take place before Hamas fully disarms. Kushner was said to have told Netanyahu not to create obstacles to a peace deal, US officials told media outlets.

Trump has staked the political legacy of his second presidential term as being the "peacemaker-in-chief", but his efforts to disengage the US from conflicts across the Middle East are stalling.

The US president delivered the threat against Oman as he struggles to draw the conflict to a conclusion, almost six months after it was launched, and as a diplomatic window agreed with Tehran ran out with no final agreement in sight. But Trump also claimed during Monday's interview that he was "not in a hurry" to reach a deal.

That two-month window for a negotiated settlement closed on Monday without a breakthrough. Trump has repeatedly claimed the war would end "soon", and talked up the prospect of a lasting peace deal in recent months, without such a breakthrough materialising.

In the same interview, Trump said Iran should "put up the white flag of surrender", but signalled he was not about to impose a fresh deadline on Tehran. "I have no time schedule. I'm not in a hurry," he said.

Trump signed a memorandum of understanding with Iran at the Palace of Versailles on 17 June, on the sidelines of the G7 summit, which had paused hostilities and set a maximum 60-day window – extendable only by mutual consent – for the two sides to reach a comprehensive deal covering sanctions relief, Iran's nuclear programme and other disputes.

Trump also dismissed concerns that Washington's own arsenal was being depleted by nearly six months of fighting, telling Fox News that what the US had expended against Iran so far was "peanuts".

He suggested many of the US's more advanced munitions, including air defence systems, had already been "given away" to Ukraine under his predecessor, Joe Biden – a claim that echoes warnings from defence analysts earlier in the war that US and allied stockpiles were being drawn down faster than they could be replenished.

The remarks came after Trump used his Truth Social platform to restate his negotiating red line. "The number one Goal is, and always will be, that Iran cannot have, in any way, shape, or form, a Nuclear Weapon," he wrote.

The strait of Hormuz – a crucial chokepoint for global trade, through which about a fifth of the world's seaborne oil supplies typically pass – has been all but closed since the US and Israel launched their war on Iran in February.

Iran is to the north of the strait. Oman is to the south. The two countries have been in talks over control of the strait.

In a casual aside at a cabinet meeting in May, the president also threatened to "blow up" Oman if it failed to "behave".

It comes after Trump also threatened to declare the strait of Hormuz as "a territory of the United States" during a speech on Friday.

In addition to Oman's decades-long military and economic ties with the US, the Gulf nation of 5.3 million people has played a mediation role in the war and has itself come under attack from Tehran.

Iran's foreign ministry said on Monday that talks with Oman were "continuing in earnest", despite Trump's latest outburst.

Trump also confirmed for the first time that Washington had opened a direct backchannel to Iran's Islamic Revolutionary Guard Corps (IRGC), which the US and Israel have targeted throughout the conflict.

"They're good poker players, but they're dying," he said of the IRGC leadership.