The five Iranians were detained during a raid in the northern Iraqi city of Arbil last week.
The US military says the men are linked to Iran's Revolutionary Guard.
Tehran insists the detainees are consular officials and has demanded their release.
Zebari told CNN that the Iranians were not working out of an official consulate but a "liaison office" that Baghdad and the Kurdish regional government were aware of.
"We have communicated with the US embassy and the command of the multinational forces seeking their release if they are found not guilty," Zebari said.
He also stressed that Iraq was "not a party" to the investigation of the detainees by US forces.
Zebari said the detainees were members of Iran's Revolutionary Guards, which "is part of the Iranian political system" and "very effective and very influential in running [Iran's] foreign policy. That is the reality of Iranian politics".
The US administration has stepped up the rhetoric against Iran and has repeatedly accused it of "meddling" in Iraq.
|"If we catch your people inside [Iraq] harming US citizens or Iraqi citizens you know we will deal with them."|
the US president
Bush told CBS television's '60 minutes' programme on Sunday that Iran would be empowered if the US was defeated in Iraq, and that world peace would be threatened.
He issued a warning to Mahmoud Ahmadinejad, the Iranian President, saying: "If we catch your people inside [Iraq] harming US citizens or Iraqi citizens you know we will deal with them."
Dick Cheney, the US vice president, earlier told the Fox television network that Iran should "keep their folks at home" and not try to destabilise Iraq.
Ahmadinejad, who is currently visiting south America, said the US is trying to hide its failures in Iraq by accusing his country of funding Iraqi fighters.
Bush also used the CBS interview to defend, for the second time this week, his plan to send 21,500 extra troops to Iraq.
The president has said he will go ahead with deployment no matter how much opposition he faces from the US Congress.
"I fully understand they could try to stop me," Bush said. "But I've made my decision, and we're going forward."
Barack Obama, a Democratic Senator and possible presidential candidate in 2008, said: "We need to look at what options we have available to constrain the president."
Democrats are wary of appearing unsupportive of American troops but are considering cutting off funding for sending additional soldiers to Iraq.
It is unclear, however, how any effort by Congress could affect Bush's plan.
Stephen Hadley, the US national security adviser, said the White House already has money appropriated by Congress to move the troops to Iraq.