By Phil Stewart and Idrees Ali

WASHINGTON (Reuters) - The Pentagon on Tuesday warned that whoever fired missiles at a U.S. Navy destroyer and an accompanying ship off the coast of Yemen over the weekend had done so "at their own peril," language that suggested preparations for possible retaliation.

Two shore-launched cruise missiles, which U.S. officials believe were designed to hit vessels at sea, were fired at the U.S. Navy ships on Sunday from Houthi-controlled territory of Yemen, just north of the Bab al-Mandab strait.

Both failed to hit the ships but the attack, which was first reported by Reuters, could deepen U.S. involvement in Yemen. U.S. military action in the country has largely been reserved for the battle against al Qaeda's affiliate, al Qaeda in the Arabian Peninsula, not the Houthis.

"Anybody who takes action, fires against U.S. Navy ships operating in international waters, does so at their own peril," Pentagon spokesman Captain Jeff Davis told a news briefing.

Asked whether the Pentagon was developing targets for retaliatory strikes, Davis said: "I'm not confirming that right now."

U.S. support for a Saudi Arabia-led coalition battling the Houthis has been reduced in recent months, and had been under review amid growing concerns about civilian casualties in Yemen's war. It includes refueling Saudi jets that are carrying out strikes.

The Houthis, allies of Iran who drove the Western- and Saudi Arabia-backed President Abd Rabbu Mansour al-Hadi from the capital in 2014, have denied firing at the USS Mason guided missile destroyer and the USS Ponce, an amphibious transport dock.

But U.S. officials have told Reuters that Washington is operating under the assumption that Houthi forces fired the cruise missiles on Sunday.

Davis suggested as much on Tuesday, noting that the Houthis had previously acknowledged responsibility for firing on a vessel from the United Arab Emirates a week earlier.

"The Houthis have said publicly before that they would target any ships in that area that were supporting the coalition against them," Davis said.

"So the facts certainly seem to point to it, but we are still assessing and we will have more for you."

The strikes against the UAE and U.S. vessels risks disrupting commercial traffic through the Bab al-Mandab strait, one of the world's busiest routes.

While shipping companies have yet to divert vessels, there are growing worries that an escalation could hinder oil supplies and lead to higher insurance costs. Nearly four million barrels of oil are shipped daily through the Bab al-Mandab gateway to Europe, the United States and Asia.

The UN last week said it took threats to shipping around Bab al-Mandeb "extremely seriously."

(Additional reporting by Mohammed Ghobari and Jonathan Saul; Editing by Alan Crosby)