Yemen's Houthi rebels on Thursday denied they had fired at a US navy ship, hours after Washington said it launched retaliatory strikes against three radar stations in rebel-controlled areas.

"The Yemeni army and Popular Committees [a rebel militia] are fully ready to cooperate with any United Nations or international body to investigate these claims," said Sharaf Luqman, a spokesman for the pro-rebel army forces.

He condemned the bombing of Houthi-controlled radar sites off the Red Sea, thought to be the first direct strikes by the US against the rebels.

"The direct American aggression and targeting the Yemeni lands today is unacceptable," Luqman added, according to Yemen's rebel-controlled Saba news agency.

The strikes, authorized by President Barack Obama, came in response to a failed attack on a US navy ship on Sunday, which was launched from Houthi territory, the Pentagon said.

A naval vessel had detected two inbound missiles, however both fell short of their target and hit the water, according to a Pentagon statement.

"The United States will respond to any further threat to our ships and commercial traffic ... and will continue to maintain our freedom of navigation in the Red Sea," a Defence Department statement said.

The bombardment was the first known to have been carried out by the US against Houthi targets in Yemen since Washington’s ally, Saudi Arabia, started an a air campaign against Iran-allied rebels in March 2015.

The failed attack on the US vessel came a day after at least 140 people were killed in airstrikes on a funeral hall in Yemen's rebel-controlled capital Sana'a. 

The Houthis accused the Saudi-led coalition of the attack, an accusation denied by the alliance.

Saudi Arabia fears that Yemen's mostly Shiite rebels will give its regional rival, Shiite Iran, a strategic foothold on the Arabian Peninsula.

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