ABOARD AIR FORCE ONE, Aug 2 (Reuters) - Kofi Annan's resignation on Thursday as international peace envoy for Syria underscores Syrian President Bashar al-Assad's refusal to abide by a U.N.-backed peace plan and the failure of Russia and China to hold Assad accountable at the U.N. Security Council, the White House said.

"President Assad, despite his promise to abide by the Kofi Annan plan, continues to brutally murder his own people, to use heavy weapons in assaults on civilian population centers," White House spokesman Jay Carney told reporters aboard Air Force One on Thursday as President Barack Obama headed to Florida.

The Obama administration recently has already begun shifting its focus away from deadlocked U.N. diplomacy over Syria and is seeking to further bolster Syrian rebel forces.

In the wake of Annan's decision to step down, Carney insisted that Washington remained committed to the belief that "Assad must go" but made clear that U.S. aid to rebels will still stop short of supplying them with weapons.

Saying Obama was "grateful for Kofi Annan's willingness to serve," Carney appeared to assign some of the blame for the failed peace mission not only to Assad but to Russia and China's resistance to further U.N. sanctions against the Syrian leader.

"Annan's resignation highlights the failure at the United Nations Security Council of Russia and China to support resolutions, meaningful resolutions, against Assad that would have held Assad accountable," Carney said.

He reiterated the U.S. position that Moscow and Beijing's double veto "were highly regrettable and place both Russia and China on the wrong side of history, and on the wrong side of the Syrian people."

Obama has signed a secret order authorizing U.S. support for rebels seeking to depose Assad and his government, U.S. sources familiar with the matter have told Reuters.

Obama's order, known as an intelligence "finding," broadly permits the CIA and other U.S. agencies to provide support that could help the rebels oust Assad.

But asked about the idea of arming the rebels, Carney said: "Our position has not changed. We provide non-lethal assistance to the opposition. We don't believe that adding to the number of weapons in Syria is what's needed to help bring about a peaceful transition." (Reporting By Margaret Chadbourn, Writing by Matt Spetalnick and Laura MacInnis; Editing by Sandra Maler)