KABUL, Afghanistan — Six American service members and at least a dozen civilians died in attacks Saturday in Afghanistan's east and south, adding to a summer of escalating violence as Taliban militants push back against stepped-up operations by international and Afghan forces.

NATO said four U.S. service members died in the east: One as a result of small-arms fire, another by a roadside bomb, a third during an insurgent attack and the last in an accidental explosion. Two other U.S. troops died in separate roadside bombings in southern Afghanistan.

Their deaths raised to 23 the number of American troops killed so far this month in the war.

Also, unknown gunmen killed 11 Pakistani Shia tribesmen in the east and at least one person died when a bomb planted on a motorbike exploded in Kandahar city in the south, officials said.

Explosions also hit two convoys of international troops in different parts of the country, with Germany saying two of its troops were wounded by a roadside bomb in the northern province of Kunduz. Another explosion targeted NATO troops in Khost in the east, but the alliance said there were no casualties.