Deputy Defense Secretary Ashton Carter speaking at the U.S. Embassy in Seoul, South Korea, in March. Carter announced Thursday that he is stepping down in December. (Lee Jin-man/AP)

Deputy Defense Secretary Ashton B. Carter, a former contender to run the Pentagon during President Obama’s second term, announced Thursday that he will step down in December.

In his resignation letter, Carter, 59, simply stated that “it is time for me to go” but did not give a specific reason for leaving.

A theoretical physicist and former Harvard professor, Carter has been a fixture at the Pentagon under Democratic presidents; he served as assistant secretary for international security policy during the Clinton administration. But he was passed over for the top job at the Defense Department in January when Obama picked former senator Chuck Hagel (Neb.), a Republican.

Carter stayed on as deputy secretary — the No. 2 position at the Defense Department, responsible for the day-to-day management of its 2.2 million employees — over the past 10 months at Obama’s request. But many defense officials and analysts viewed Carter as an uncomfortable understudy to Hagel, given his own ambitions to lead the Pentagon.

In his letter, Carter said he had “long firmly intended” to leave the Pentagon by December. But he said he kept quiet about his plans because of “the turbulence surrounding the fiscal situation,” an apparent reference to the federal government shutdown and other forced budget cuts confronting the military.

Carter’s resignation was first announced in a statement by Hagel, who said he met with his deputy Thursday “and reluctantly accepted his decision to step down.”

“Ash has been an extraordinarily loyal and effective Deputy Secretary,” Hagel wrote. “The Department will miss him — I will miss him.”

Carter did not say what he plans to do next. And Hagel did not say who will replace him.

A brainy and amiable veteran of the national-security establishment who also holds a bachelor’s degree in medieval history, Carter joined the Obama administration in 2009 as the Pentagon’s chief weapons buyer, giving him huge influence over the nation’s military contractors.

In October 2011, he was promoted to the Pentagon’s second-ranking civilian by then-Secretary Leon E. Panetta. He was among those the White House considered to take over when Panetta announced his retirement at the end of Obama’s first term. But Hagel, a Vietnam combat veteran who served with Obama in the Senate, had superior political credentials.

Over the past year, Carter has overseen the military’s efforts to cope with shrinking and uncertain budgets after more than a decade of war, as well as a major review of military strategy commissioned by Hagel.