The reservists are from a fuel platoon that is part of the 343d Quartermaster Company, based in Rock Hill, S.C. The unit delivers food, water, and fuel on trucks in combat zones.
The episode was first reported in yesterday's editions of The Clarion-Ledger newspaper in Jackson, Miss.
A commanding general has ordered the unit to undergo a ''safety-maintenance stand down," during which it will conduct no further missions as the unit's vehicles undergo safety inspections, the military said.
On Wednesday, 19 members of the platoon did not show up for a scheduled 7 a.m. meeting in Tallil, in southeastern Iraq, to prepare for the fuel convoy's departure a few hours later, the military statement said.
''An initial report indicated that some of the 19 soldiers [not all] refused to participate in the convoy as directed," the military statement says.
The Clarion-Ledger, citing interviews with relatives of some of the soldiers, said platoon members refused to go on Wednesday's mission because their vehicles were in poor condition and they had no capable armed escort. They were going to Taji, which is north of Baghdad.
The mission was ultimately carried out by other soldiers from the 343d, which has at least 120 soldiers, the military said.
A whole unit refusing to go on a mission in a war zone would be a significant breach of military discipline. The military statement called the episode ''isolated" and called the 343d an experienced unit that performed honorable service in nine months in Iraq.
US military officials said the commanding general of the 13th Corps Support Command, Brigadier General James E. Chambers, had appointed his deputy, Colonel Darrell Roll, to investigate. An investigative team under Roll is in Tallil, questioning soldiers, the military said.
''Preliminary findings indicate that there were several contributing factors that led to the late convoy incident and alleged refusal to participate by some soldiers. It would be inappropriate to discuss those factors while the investigation continues," the military statement said.
Separately, the commander of the 300th Area Support Group, listed on a military website as Colonel Pamela Adams, has ordered a criminal inquiry to determine if any soldiers committed crimes under the Uniform Code of Military Justice, and, if so, whether disciplinary measures are warranted.
Family members told The Clarion-Ledger several platoon members had been confined, but the military did not confirm that.
The platoon has soldiers from Alabama, Kentucky, North Carolina, Mississippi, and South Carolina, said Teresa Hill of Dothan, Ala., who told the newspaper her daughter Amber McClenny is among those being detained.
Patricia McCook, of Jackson, Miss., said her husband, Staff Sergeant Larry O. McCook, was also among those detained.
She said he told her in a telephone call that he did not feel comfortable taking his soldiers on another trip.