The chairman of the Senate Armed Services Committee said Tuesday that the Defense Department could head off far deeper budget reductions by preemptively agreeing to cut $10 billion a year for the next decade.

Sen. Carl Levin, the Michigan Democrat who heads the powerful committee, said “defense has to contribute” to a compromise to head off the across-the-board, $55-billion-a-year cuts required by the budget compromise that Congress reached last year. The provision, known as sequestration, will be triggered on Jan. 3 if Congress doesn’t come up with a 10-year, $1.2 trillion deficit reduction plan or a compromise to change the law by the end of this year.

Levin suggested that some cuts could come from the costs of maintaining and modernizing the nuclear stockpile and funding for family housing for troops stationed in South Korea.

Levin, participating in a National Press Club session, said a signal should be sent on a compromise before the fiscal year ends Sept. 30, because major defense contractors have already sent “warning notices” to employees of possible cuts.

“That kind of instability and uncertainty is what is going to drive us, hopefully . . . to at least take some steps down the path of avoiding that train wreck,” Levin said.

David Langstaff, president of defense contractor TASC, told the gathering that the situation “has business standing on the sidelines waiting to see what will happen.”

Levin, who is working with other senators to come up with a compromise, called his proposed reduction of $100 billion from the Pentagon over 10 years “a figure . . . for totally planning purposes when we look at how to come up with plans to avoid sequestration.”

He described sequestration as “mindless budgeting,” where “automatic reductions, perhaps 8 percent to 10 percent,” will take place across the board. Instead, Levin said any cuts beyond the $487 billion built into the 2011 congressional compromise will have to be “prioritized, prudent, [and] no area can be exempt.”

Navy Capt. John Kirby, a Pentagon spokesman, said Tuesday, “Any cuts beyond those already factored in would require a reassessment of the strategy.”

One area Levin described as “ripe for cuts” is the nuclear stockpile. About $200 billion is being planned to modernize the nuclear weapons-building complex and build a new triad of strategic bombers, missile-launching submarines and land-based ICBMs.

Levin also suggested the possibility of savings in South Korea, where he said the United States cannot afford plans to provide family housing for dependents of American troops assigned there.

Gen. James Cartwright, former vice chairman of the Joint Chiefs of Staff, who was at the session, said a funding review for U.S. forces in South Korea is called for. “It’s time, really, to make an adjustment on the [U.S.] posture,” he said.