June was the deadliest month for the allied force since the war began in October 2001 with 102 deaths, more than half of them Americans.
Britain's Ministry of Defense reported that a Royal Marine was killed Thursday in southern Afghanistan - the fifth international service member killed this month. Petraeus called for troops and civilian staff employees to work together, saying, "In this important endeavor, cooperation is not optional."
His predecessor, Gen Stanley McChrystal, was fired last month for intemperate remarks he and his aides made to Rolling Stone magazine about Obama administration officials, mostly on the civilian side.
"Civilian and military, Afghanistan and international, we are part of one team with one mission," Petraeus told about 1,700 invited guests, including Afghan government and military and police officials gathered at the US Embassy for a pre-Fourth of July celebration marking American independence.
They were Petraeus' first public comments since he arrived Friday night to take command of US and NATO forces in Afghanistan. He said he would work to improve coordination between troops on the battlefield and civilians trying to bolster the Afghan government and improve the lives of the people.