The top U.S. defense officials, Defense Secretary Leon Panetta and Chairman of the Joint Chiefs of Staff Admiral Mike Mullen, are cautioning U.S. lawmakers against mandating more budget cuts to the military.  

In his first official briefing in the Pentagon as the new U.S. defense secretary, Leon Panetta told reporters Thursday that he believes the military can manage its $350 billion in budget cuts signed into law by President Barack Obama earlier this week.

But he warned that he thinks it would be "completely unacceptable" if the U.S. military was, as he put it, "hollowed out," by additional, across-the-board cuts to spending. "That approach would be particularly harmful because we are a nation at war.  We face a broad and growing range of security threats and challenges that our military must be prepared to confront.  From terrorist networks, to rogue nations, to dealing with rising powers that always look at us to determine whether or not we will in fact maintain a strong defense," Panetta said.

These further budget cuts would happen across government agencies, in what Panetta calls a "doomsday mechanism" included in the deal to raise the debt ceiling.  However, the automatic cuts would only occur if lawmakers cannot come up with a plan for more targeted cuts to spending in the future.

Speaking alongside Panetta, Chairman of the Joint Chiefs of Staff Admiral Mike Mullen addressed the prospect of what could be nearly $1 trillion in military spending cuts over the next 10 years if lawmakers cannot agree. "We've looked into that abyss, if you will, and we know that that is, my view is, the service chiefs' view is that is very dangerous for the country," Mullen said.

Mullen repeated his view that the U.S. debt is the greatest national security threat.  He said military programs that are behind schedule and over budget are under much scrutiny as the military tries on its own to cut costs.

Panetta also urged lawmakers to look away from the defense spending and consider making concessions on entitlement programs, which account for most of the federal budget, and increasing taxes as they seek ways to save more money.

And despite acknowledging the fact that the United States is involved in two wars, a NATO-led operation in Libya and disaster relief missions abroad, both defense leaders vowed to work with President Obama and lawmakers to do everything they can to cut costs.