The statement came a day after the US military said seven marines were killed in two separate attacks west of Baghdad on Monday.
Ansar al-Sunna said in the Internet posting that it had killed some of the marines by "slitting their throats," while others were shot. The statement could not be verified.
It also said that its fighters had captured a ninth US marine "who was wounded in an ambush... near Haditha," a town which lies 250 kilometresmiles) west of Baghdad,
The group vowed to publish more details on the killings and pictures of the "American prisoner" later.
Ansar al-Sunna has claimed a string of attacks in Iraq, including murders of foreign hostages and Iraqis accused of "collaborating" with US-led forces.
The total number of US military personnel killed in Iraq since the March 2003 US-led invastion stood at 1,787 as of Monday, according to the Pentagon.