They were held on suspicion of being "closely tied to activities targeting Iraqi and coalition forces," it said
According to Iranian state television, Tehran's embassy in Baghdad has sent a note to Iraq's foreign ministry calling for the immediate release of the arrested staff members.
A Kurdish TV station said Kurdish security forces took over the building after the Americans left the area.
Hoshyar Zebari, a Kurd and Iraq's foreign minister, said on Friday that the Iranians were working in a "liaison office" in Arbil with government approval and was in the process of being approved as a consulate.
Iraqi and Iranian officials initially had said the Iranian office was a diplomatic mission, which would have raised questions about whether those detained Thursday had diplomatic immunity'Disturbance and condemnation'
The offices of the Kurdish prime minister and Kurdish president expressed their "disturbance and condemnation" at the pre-dawn operation and urged the US military to release employees arrested during the raid.
Mohammad Ali Hosseini, the Iranian foreign ministry spokesman condemned the raid and said it was a violation of international law.
|"There is no justification for this behaviour of the Americans, particularly because Iraqi officials were not informed about this move."|
Mohammad Ali Hosseini, Iranian foreign ministry spokesman
"The activity of all those people at our office in Arbil was legal and was in co-operation with, and had the approval of, the Iraqi side," Hosseini told Iran's state-owned Arabic language satellite channel Al-Alam.
"There is no justification for this behaviour of the Americans, particularly because Iraqi officials were not informed about this move," he added.
On Thursday, Condoleezza Rice, the US secretary of state, warned Iran that the United States would not "stand idly by" if Tehran tries to disrupt Washington's renewed effort to stabilise Iraq.
Speaking just hours after the Arbil raid, Rice said Washington was determined to crack down on Iran's "regional aggression".
US officials have repeatedly accused Iran of interfering in Iraq and supplying Shia militias with weapons.
In December, US forces in Baghdad arrested a number of Iranians they said were suspected of planning attacks on Iraqi security forces, including diplomats who were later turned over to Iraqi authorities.