TEHRAN : Iran and the United States held their fire Sunday, handing Gulf shipping and the oil industry a respite from missile strikes as Donald Trump's UN envoy said the president was "giving talks some space".

Iran said it had halted retaliatory attacks against Washington's allies in the Middle East, and US ambassador to the United Nations Mike Waltz told "Fox News Sunday" that, while forces remained "locked and loaded", Trump would give negotiations "a little bit of room".

Oil prices fell on Asian markets early Monday as investors breathed cautious sighs of relief at the pause in combat.

About half an hour into trading, the price of a barrel of international benchmark North Sea Brent crude was down 5.89 percent to $91.08, after briefly dipping below the $90 mark. US counterpart West Texas Intermediate slid 5.73 percent to $84.19.

Prior to Friday, the US military had carried out strikes on Iran for 13 consecutive nights, in the largest rekindling of the almost five-month-old war since an April ceasefire. Friday and Saturday nights passed without bombing.

"These attacks continued until two nights ago, but over the past two nights the Americans have stopped their attacks," said Iran's army spokesman Mohammad Akraminia.

"Since... our strategy has essentially been retaliatory, we have also halted our retaliatory operations."

Fighting over the strategic Strait of Hormuz derailed diplomatic efforts between Washington and Tehran, but the conflict then expanded beyond the vital energy corridor to include attacks on US bases, regional shipping and Gulf allies.

Unconfirmed Iranian media reports on Sunday said an oil tanker had been damaged by a sea mine.

- 'One way or the other' -

The lull has revived hopes of a return to negotiations, although American media reported the pause could also reflect pressure on US stockpiles of Patriot interceptors and other defensive weapons.

Waltz dismissed this idea, in a second interview with NBC News' "Meet the Press".

"I want to be crystal clear. The US military -- and I've verified this every which way -- has everything that it needs to conduct this campaign as effectively as it needs to be," he insisted.

Israel's Prime Minister Benjamin Netanyahu is due at the White House on Tuesday, and is expected to urge Trump to continue to take a tough line on Tehran, in particular on its nuclear programme.

Iran has long insisted the programme is for civilian purposes but the US and its allies allege it is aimed at developing a weapon.

Also speaking to Fox News, Netanyahu said he fully backed Trump's efforts to shut down Iran's nuclear programme.

"If he can do so without returning to intense military fighting, that's fine. Why not? But one way or the other, they have to end their nuclear programme, and with a deal or without a deal, that has to come to an end," he said.

Plans to escalate the US campaign have been shelved in part because of shrinking munitions supplies, The New York Times reported, citing two people briefed on the matter.

- New front -

Trump also faces the risk of a wider Middle East war, the estrangement of vulnerable Gulf allies and further shocks to the global economy, the newspaper said.

Trump said on Friday he had not decided whether to return to an all-out operation.

"We're talking to them right now. I think they're getting more and more serious," he told journalists.

The war that Trump once predicted would last four or five weeks is now nearing its fifth month and weighing on the Republican's approval ratings ahead of crucial US midterm elections in November.

On Sunday locals in Tehran carried on with a normal day, dealing with heavy traffic jams on their way to work, an AFP journalist said.

Shops and restaurants were open as usual as the city suffered a heatwave.

Fighting has meanwhile spread to a new front.

Iran-backed Houthi rebels on Sunday said they downed a Saudi drone over northwestern Yemen, a day after the Yemeni group claimed it attacked oil facilities in the Gulf kingdom.

The Houthis had said they struck Saudi Aramco sites in Jizan and Yanbu, after Riyadh bombed Houthi targets on Friday.