SANAA, Yemen — The turmoil in Yemen grew into a regional conflict Thursday, with Saudi Arabia and its allies bombing Shiite rebels allied with Iran, while Egyptian officials said a ground assault will follow the airstrikes.

Iran denounced the Saudi-led air campaign, saying it “considers this action a dangerous step,” and oil prices jumped in New York and London after the offensive.

The military action turned impoverished and chaotic Yemen into a new front in the rivalry between Saudi Arabia and Iran.

Yemen’s U.S.-backed President Abed-Rabbo Mansour Hadi, who fled the country Wednesday as the rebels known as Houthis advanced on his stronghold in the southern port of Aden, reappeared Thursday. He arrived by plane in Saudi Arabia’s capital of Riyadh, Saudi state TV reported.

Starting before dawn, Saudi warplanes pounded an air base, military bases and anti-aircraft positions in the capital of Sanaa and flattened a number of homes near the airport, killing at least 18 civilians, including six children. Another round followed in the evening, again rocking the city.

Rebel leader Abdul-Malik al-Houthi angrily accused the United States, Saudi Arabia and Israel of launching a “criminal, unjust, brutal and sinful” campaign aimed at invading and occupying Yemen.