WASHINGTON  The chairman of the Joint Chiefs of Staff has written a searing critique of government efforts at “strategic communication” with the Muslim world, saying that no amount of public relations will establish credibility if American behavior overseas is perceived as arrogant, uncaring or insulting.

The critique by the chairman, Adm. Mike Mullen, comes as the United States is widely believed to be losing ground in the war of ideas against extremist Islamist ideology. The issue is particularly relevant as the Obama administration orders fresh efforts to counter militant propaganda, part of its broader strategy to defeat the Taliban and Al Qaeda in Afghanistan and Pakistan.

“To put it simply, we need to worry a lot less about how to communicate our actions and much more about what our actions communicate,” Admiral Mullen wrote in the critique, an essay to be published Friday by Joint Force Quarterly, an official military journal.

“I would argue that most strategic communication problems are not communication problems at all,” he wrote. “They are policy and execution problems. Each time we fail to live up to our values or don’t follow up on a promise, we look more and more like the arrogant Americans the enemy claims we are.”