As Saudi Arabia carried out airstrikes in Yemen Wednesday against Houthi forces, an official from the Shiite rebel group said they would exact revenge on “the Zionist Saudi regime,” the Israeli Ynet news site reported.

Saudi Arabia launched an operation early Thursday to save the government of embattled President Abedrabbo Mansour Hadi as the country teetered on the brink of civil war after the Iran-backed separatists overran the southern stronghold of Aden.

The Houthi official promised there would be no pilgrimage to the holy Saudi city Mecca this year.

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Another Houthi official, a member of the Houthi political council, said on Al-Jazeera that “we will threaten you in your own homes.”

Anti-Zionist and anti-Jewish rhetoric is common among the Houthis. The slogan “Death to Israel. A curse on the Jews.” is common on flags and other propaganda materials.

Last week, video of the bombing of a Houthi mosque in Yemen showed the crowd chanting “Death to America. Death to Israel. Curse upon the Jews. Victory to Islam. Allahu Akbar,” before a suicide bomber detonated himself, killing scores.

The United States is coordinating closely with Saudi Arabia and regional allies in the military action against Houthi rebels in Yemen, including providing intelligence and logistical support, the White House said Wednesday.

“President Obama has authorized the provision of logistical and intelligence support to GCC-led military operations,” National Security Council spokeswoman Bernadette Meehan said in a statement, referring to the Gulf Cooperation Council.

Condemning the Houthi rebels, a Shiite militia that launched a power grab in the Yemeni capital Sanaa in February, Meehan said Washington had also been in close contact with the embattled Hadi.

US forces were not taking direct military action in Yemen, she stressed, but were “establishing a Joint Planning Cell with Saudi Arabia to coordinate US military and intelligence support.”

“We strongly urge the Houthis to halt immediately their destabilizing military actions and return to negotiations as part of the political dialogue,” added Meehan.

“The international community has spoken clearly through the UN Security Council and in other fora that the violent takeover of Yemen by an armed faction is unacceptable and that a legitimate political transition — long sought by the Yemeni people — can be accomplished only through political negotiations and a consensus agreement among all of the parties.”

Two senior US Republican senators, John McCain of Arizona and Lindsey Graham of South Carolina, endorsed the attacks. But they also used the occasion to criticize what they called a lack of US leadership in the region.

“We understand why our Saudi and other Arab partners felt compelled to take action. The prospect of radical groups like Al-Qaeda, as well as Iranian-backed militants, finding safe haven on the border of Saudi Arabia was more than our Arab partners could withstand,” the senators said in a joint statement.

“Their action also stems from their perception of America’s disengagement from the region and absence of US leadership,” they wrote.