The United States and Yemen's Houthi rebels have reached a ceasefire agreement, mediator Oman announced Tuesday, saying the deal would ensure "freedom of navigation" in the Red Sea where the Iran-backed rebels have attacked shipping.

It comes after President Donald Trump announced that the United States would end its attacks against the Houthis after the Iran-backed rebels agreed to stop harassing ships in the Red Sea, though he made no direct mention of recent attacks on ally Israel.

Omani Foreign Minister Badr Albusaidi said that "following recent discussions and contacts... with the aim of de-escalation, efforts have resulted in a ceasefire agreement between the two sides".

"Neither side will target the other... ensuring freedom of navigation and the smooth flow of international commercial shipping" in the Red Sea, he added in a statement posted online.

In surprise comments at the White House, Trump said the Iran-backed rebels had "capitulated" after a near-daily, seven-week US bombing campaign that left 300 dead, according to an AFP tally of Houthi figures.

"The Houthis have announced... that they don't want to fight anymore. They just don't want to fight," Trump said during a White House press appearance with Canadian Prime Minister Mark Carney.

"And we will honour that, and we will stop the bombings, and they have capitulated," he added.

"They say they will not be blowing up ships anymore, and that's... the purpose of what we were doing," the US president said, adding that the information came from a "very, very good source".

Trump's comments came just hours after Israeli warplanes put rebel-held Sanaa's international airport out of action in a series of raids that killed three, according to the Houthis.

The Pentagon said last week that US strikes had hit more than 1,000 targets in Yemen since mid-March.

Shortly after Oman's announcement, the head of Yemen's Houthi Supreme Political Council, Mahdi al-Mashat, said the Iran-aligned group will continue their attacks to support Gaza, Houthi-affiliated Al Masirah TV reported.

He asked Israelis to "remain in shelters because their government will not be able to protect them", indicating the ceasefire with the US did not include a halt of the group's attacks on Israel.