During an official visit to Tehran on August 3, Zebari said Iran had been bombarding Kurdish villages in northern Iraq for two weeks.
Zebari said the bombardment had forced as many as 3,000 Kurdish villagers to flee their homes in the Iran-Iraq border area.
Zebari told reporters in Tehran that “in a normal relationship between two countries, this amounts to an act of aggression.”
Tehran has so far refused to publicly acknowledge any such activity.
But Zebari quoted Iranian Foreign Minister Manuchehr Mottaki as saying privately in a meeting that the shelling was in response to attacks by a Kurdish-Iranian guerrilla group -- Pezak -- that maintains bases in the rugged mountains of northern Iraq.
Zebari described the Iranian shelling as indiscriminate and said it was achieving little against Pezak positions. Members of Pezak are said to seek autonomy for Kurds in Iran.
The government of the Kurdish-administered region of northern Iraq has also been sharply critical of both Iran and Turkey for cross-border shelling.
"We strongly condemn this Iranian-Turkish shelling, and we demand that Turkey and Iran cease it immediately, and especially we demand that from Iran because it crossed all limits with its hostile actions," the region's president, Mas'ud Barzani, said to the regional parliament in Irbil: "This shelling will not be in our common interest, and we never expected that Iran would act in such a manner against the Kurdish people."
Turkey is reported to be shelling Kurdish villages in northern Iraq, where it says fighters from the Kurdistan Workers Party (PKK) fighting against Ankara are finding shelter. Some reports say that Turkey presently has an estimated 140,000 troops near its border with northern Iraq.
Dilemma For U.S.
Yahia Said, a researcher at the London School of Economics who has several times traveled to Iraq, says Iran's actions can be understood.
"Iran has problems with [its] Kurdish minority just as Turkey does, though of less intensity," Said says. "And obviously they are concerned about eventual independence or autonomy in Iraqi Kurdistan and what impact it will have. So they are trying, probably, to intimidate Kurdish parties."
Said says he does not believe the shelling will escalate into an open conflict but is more an effort to make Iraqi Kurdish parties do something about the situation.
Zebari also has said that the Kurd-dominated national army in the northern region should control Kurdish groups coming from neighboring countries.
However, many of those troops are committed to security operations in other parts of the country, and the Kurdish autonomous government is short of troops to send to the border regions.
Said says the United States is in no position to stop the shelling into northern Iraq from Iran and Turkey.
Kurdish guerrillas on the Iraqi side of the border with Iran (AFP)
"I don't think the U.S. can stop Turkey from shelling Iraq actually. I'm not even sure they are applying any pressure on them [Turks]," he says. "Relationships have been very delicate ever since Turkey refused to support the  invasion [of Iraq]. The U.S. is in a very weak position to stop the shelling, because they are targeted at allegedly terrorist groups, who have been engaged in terrorist activity in both Iran and Turkey. So, from a moral perspective it is very difficult for the U.S."
The "The New York Times" reports today that the Iraqi government previously sent a letter of protest to Iran about the shelling.
The newspaper quotes the Iraqi ambassador to Iran, Mohammad Majid al-Sheikh, as saying “we have not received any sensible response from them.”
(Radio Free Iraq contributed to this story)