The Afghan interior minister, Ahmad Jalali, confirmed that three foreigners and four Afghans were detained after a brief shootout on Monday.
Jalali told a news briefing that the "rebel" group had been illegally detaining and interrogating locals.
"They apparently said that their aims were to act against those carrying out terrorist attacks ... but they did not have a legal relationship with anyone and the United States was also chasing them - they are actually rebels."
The US embassy said the three had identified themselves as American, but that this was still to be confirmed.
Spokesman Roy Glover believes their names may be Jonathan Idema, Edward Caraballo and Brent Bennett. The three had been passing themselves off as US government or military officials.
Plain-clothes US agents and private security contractors are a common sight in Kabul, but the military has issued a statement denying any connection with the men.
"The public should
be aware that Idema does not represent
government and we do not employ him"
US military statement
"The public should be aware that Idema does not represent the American government and we do not employ him," a statement said.
Jalali said the group, wearing local and foreign military uniforms, had illegally held eight people - who were found in the group's hideout after the raid.
News of the arrests comes when the US military has been under scrutiny for its treatment of prisoners in Afghanistan, where it has been accused by Human Rights Watch of "systematic" abuse of detainees.
The military said on Wednesday that it had completed a review of conditions in its Afghan detention centres and parts would be released after submission to the US Congress.
The military says it has investigated five deaths of prisoners in Afghanistan since August 2002 and last week said it was looking into a new allegation of prisoner abuse.
Last month, a CIA contractor was arrested on charges of beating a detainee who died in 2003, the first indictment brought in connection with prisoner abuse in Afghanistan.