Rice's comment came after U.S. forces early on January 11 raided an Iranian diplomatic office in the northern Iraqi city of Irbil, detaining five people and seizing computers and documents.
It also follows a stern warning from the top military adviser to U.S. President George W. Bush, in which General Peter Pace claimed that "it is clear that the Iranians are complicit in providing weapons, and it is also clear that we will do all we need to do to defend our troops in Iraq by going after the entire network, regardless of where those people come from."
U.S. officials say the Iranians detained in Irbil, in Iraq's northern Kurdish region, are suspected of being involved in anti-Iraqi activities.
U.S. Ambassador to Iraq, Zalmay Khalilzad, said the Iranians were being questioned, but he did not give more details.
Meanwhile, Iraqi Foreign Minister Hoshyar Zebari said the Iranians were working with official sanction. But he said today that their "liaison office" in Irbil was not a full consulate and did not enjoy diplomatic protection.
The arrests drew condemnation from Tehran, but also from Iraq's regional Kurdish government, which said it "was not aware in advance of the raid."
Connections With Iran
Many Kurds, including Iraqi President Jalal Talabani, had close ties to Iran before the U.S.-led invasion in 2003.
Kaveh Fatah, a journalist in Irbil, speaking to Radio Farda on January 11, said the raid obviously happened without the knowledge of the local authorities and put local Kurdish and U.S. forces on the verge of confrontation. Fatah said U.S. soldiers were apparently prevented from flying the Iranians out of the city.
"The government of Iraqi Kurdistan has said that it was unaware of the incident," Fatah reported. "On the other hand, when U.S. forces wanted to transfer detainees from Irbil’s international airport to an unknown location, Kurdish security forces prevented them from doing so and said that the U.S. forces had not informed Kurdish [officials]."
It remains unclear where the detainees are currently being held.
Condoleezza Rice warned Iran on January 11 that the United States would not allow further destabilization in Iraq.
"If the government in Tehran wants to help stabilize the region, as it now claims, then it should end its support for violent extremists who destroy the aspirations of innocent Lebanese, Palestinians, and Iraqis," Rice said. "And it should end its pursuit of nuclear weapons."
In late December, U.S. troops elsewhere in Iraq detained at least two Iranians and released two others who had diplomatic immunity.
(with additional reporting by AFP, AP)