By Mark Hosenball and Matt Spetalnick

WASHINGTON, Jan 22 (Reuters) - The United States has pulled more staff out of its embassy in Yemen, U.S. officials said on Thursday as Washington scrambled to cope with the collapse of a government that had been a key ally in the fight against al Qaeda.

The officials, who spoke to Reuters on condition of anonymity, said the U.S. diplomatic contingent in the Yemeni capital Sanaa has been drawn down due to the deteriorating security situation there but that there were no plans to close the embassy.

U.S. authorities have privately made clear they want the compound, an important outpost for counter-terrorism cooperation with Yemeni forces, to remain open as a demonstration of American resolve.

But current and former U.S. officials say the chaos engulfing Yemen has already threatened the administration's strategy against a powerful al Qaeda branch there. Just four months ago, Obama had touted Yemen as a model for "successful" counter-terrorism partnerships worldwide.

Word of the withdrawal of further U.S. personnel came on the same day that Yemeni President Abd-Rabbu Mansour Hadi stepped down, throwing the country deeper into chaos days after Iran-backed Houthi rebels battled their way into his presidential palace.

The Obama administration was caught off guard by the resignation of Hadi, a key security ally of the United States who had backed American drone strikes and special forces operations against al Qaeda militants.

"We are still assessing the implications," White House spokesman Josh Earnest told reporters aboard Air Force One.

The decision to withdraw more embassy staff followed repeated public assurances from the Obama administration that it considered the safety of U.S. personnel of paramount importance.

The State Department had already reduced staff at the embassy in recent months to essential personnel, mostly related to security matters, as the fighters from the Shi'ite Houthi minority seized control of the capital.

"In response to the changing security situation in Yemen, the United States Embassy in Sanaa has further reduced its American personnel working in Yemen," a senior State Department official told Reuters.

"While the Embassy remains open and is continuing to operate, we may continue to re-align resources based on the situation on the ground. We will continue to operate as normal, albeit with reduced staff," the official said.

It was not immediately known how many U.S. staffers remained or how many would be withdrawn.

INCREASING ALARM IN WASHINGTON

Washington watched with increasing alarm in recent days as Houthi rebels held Hadi as a virtual prisoner in his official residence. U.S. officials had hoped that Hadi's announcement on Wednesday that he was ready to make concessions to the Houthi movement would calm the situation but that prospect fell apart just a day later.

Washington is concerned that the chaos in Yemen could create conditions that al Qaeda in the Arabian Peninsula (AQAP) will exploit to strengthen its base of support there and use the country to plot attacks on Western interests. AQAP claimed responsibility for deadly attacks in Paris early this month.

A former senior U.S. official said that events in Yemen will "absolutely" limit U.S. drone strikes and counter-terrorism operations in the country in the short-term and that if the Houthis ends up in full control of the government they will demand a halt to the drone campaign.

Some U.S. officials believe that while the Houthis are determined to wield more power in Yemen the movement may not want to assume responsibility for actually governing the divided, impoverished country.

But overall the Obama administration appears to have few contacts with the Houthis and remains concerned that their emergence as the country's main powerbrokers will mean greater influence for Iran in Yemen's affairs. (Reporting by Jason Szep, David Rohde, Arshad Mohammed, Patricia Zengerle; editing by Stuart Grudgings)