* Panetta draws line at more extensive future cuts

* Pentagon chief vows to fight for “common sense” (Updates with Mullen, more Panetta quotes)

WASHINGTON, Aug 4 (Reuters) - U.S. Defense Secretary Leon Panetta said on Thursday the $350 billion in security spending savings in the deficit-cutting package signed by President Barack Obama was manageable, but warned against greater cuts.

“Anything that doubles that would be disastrous to the defense budget,” he told reporters.

Panetta, in his first news conference since taking over from Robert Gates a month ago, voiced strong opposition to potential cuts in military spending of some $600 billion under a second round of the plan Obama signed on Tuesday in a deal to lift the country’s $14.3 trillion debt ceiling.

The hard-fought legislative deal calls for the $350 billion in savings over the coming decade against a Congressional Budget Office “baseline” projection, most of it likely to be borne by the Defense Department as part of at least $2.1 trillion in budget savings overall.

Under a process called sequestration, the Pentagon would face a potential second round of cuts in security spending estimated at about $600 billion from fiscal 2012 to 2021.

Asked if he would quit in the event of sequestration, Panetta said: “I didn’t come into this job to quit, I came into this job to fight and my intention is to fight to make sure that hopefully some common sense prevails here.”

Mike Mullen, the chairman of the Joint Chiefs of Staff, echoed his boss, telling reporters the “the terms of that deal are — at least in the near-term — reasonable and fair with respect to future cuts.”

But he added: “We cannot allow that effort to go so far and cut so deep that it jeopardizes our ability to deal with the other very real and very serious threats we face around the world.”

Both men vowed to work with the administration and Congress to realize the cuts.

“A balanced approach is what the chiefs and I seek and sensible cuts are what we expect,” said Mullen. (Reporting by David Alexander; editing by Philip Barbara)