After Trump made the announcement, Oman said it had mediated a ceasefire deal between the Houthis and the US, marking a major shift in the Iran-aligned group's policy since the start of Israel's war in the Gaza Strip in October 2023.
Under the agreement, neither the US nor the Houthi rebels would target the other, including US vessels in the Red Sea and Bab al-Mandab Strait, Oman said in a statement.
The statement by Omani Foreign Minister Badr Albusaidi did not mention whether the Houthis had agreed to stop attacks on Israel.
"They said please don't bomb us any more and we're not going to attack your ships," Trump said of the Houthis during an Oval Office meeting with Canadian Prime Minister Mark Carney.
"And I will accept their word, and we are going to stop the bombing of the Houthis effective immediately."
The US intensified strikes on Yemen's Houthi fighters this year, to stop attacks on Red Sea shipping.
Rights activists have raised concerns over civilian casualties.
The Houthis have been firing at Israel and at shipping in the Red Sea since Israel began its military offensive against Hamas in the Gaza Strip after the Palestinian militant group's deadly attack on Israel on October 7, 2023.
Trump said the United States will take the Houthis' word that they would not be blowing up ships any longer.
The US military has said it has struck more than 1000 targets since its current operation in Yemen, known as Operation Rough Rider, started on March 15.
The strikes, the US military said, have killed "hundreds of Houthi fighters and numerous Houthi leaders".
Tensions have been high since the Gaza Strip war began but have risen further since a Houthi missile landed near Israel's Ben Gurion Airport on Sunday, prompting Israeli air strikes on Yemen's Hodeidah port on Monday.
The Israeli military carried out an air strike on Yemen's main airport in Sanaa on Tuesday, its second attack in two days on Iran-aligned Houthi rebels after a surge in tensions between the group and Israel.
Under former president Joe Biden's administration, the US and the United Kingdom retaliated with air strikes against Houthi targets in an effort to keep open the crucial Red Sea trading route - the path for about 15 per cent of global shipping traffic.
Trump did not say whether the UK had agreed also to the ceasefire.
After Trump became US president in January, he decided to significantly intensify air strikes against the Houthis.
The campaign came after the Houthis said they would resume attacks on Israeli ships passing through the Red Sea and Arabian Sea, the Bab al-Mandab Strait and the Gulf of Aden.
On April 28, a suspected US air strike hits a migrant centre in Yemen, and Houthi TV says 68 people were killed in one of the deadliest attacks in six weeks of intensified US strikes.
