The squad was one of three belonging to the 1st Platoon of Lima Company, 3rd Battalion, 25th Regiment, according to The Washington Post, which has a reporter with Operation Matador.
Chief Warrant Officer Orrin Bowman, the site commander for the Columbus-based company, confirmed Thursday the company was participating in the operation and had taken casualties. He declined to say how many from the Marine reserve unit had been killed or release any names.
The U.S. military has confirmed five Marine deaths so far and says about 100 insurgents have been killed in the operation — one of the largest U.S. offensives since Fallujah was reclaimed from militants.
It was launched after U.S. intelligence showed large numbers of insurgents had moved into the northern Jazirah Desert following losses in Fallujah and Ramadi, farther east. The area is believed to be a staging ground for foreign fighters crossing into Iraq from Syria along ancient smuggling routes.
The offensive started Saturday night and was aimed at rooting out followers of Iraq's most wanted militant leader, Abu Musab al-Zarqawi.
The Department of Defense identified two Ohio Marines with the 3rd Battalion, 25th Regiment who have died in Iraq since Sunday: Lance Cpl. Wesley G. Davids, 20, of Dublin, was killed in an explosion in Karabilah on Wednesday, and Cpl. Dustin A. Derga, 24, of Columbus, was killed by small arms fire in Ubaydi on Sunday.