Government spokesman Ali al-Dabbagh's comments were the first official Iraqi condemnation of Sunday's raid, in which four U.S. helicopters attacked the village of Sukkariyeh, several miles inside Syria's border.
Al-Dabbagh spoke after a Cabinet meeting Tuesday that was chaired by Prime Minister Nouri al-Maliki.
He says the government "rejects" the raid even if the U.S. claims such operations are legitimate. He also says Iraq doesn't want its territory to be used for attacks in neighboring nations.
But he urged Syria to crack down on what he said are "organizations" operating on its territory that have the intention of harming Iraq.
Damascus charged that U.S. forces a civilian building under construction shortly before sundown on Sunday, killing eight.
A U.S. military official said the target was a network that smuggles fighters and weapons into Iraq.
CBS News national security correspondent David Martin reported the raid targeted and killed Abu Ghadiyah, who was a senior al Qaeda in Iraq operative responsible for funneling foreign fighters and money into Iraq.
A senior American official told The Associated Press that the U.S. operation was precipitated by intelligence that the Iraqi fugitive was planning an imminent attack in Iraq.
A U.S. official called his death "very significant."
Amateur video footage purportedly taken at the scene of the raid was released to AP Television on Tuesday, showing military helicopters flying toward the site as villagers pointed to the skies.
The grainy video was taken by a villager on a mobile phone. It does not show the helicopters landing, but shows villagers pointing in alarm as they arrive overhead.
A large crowd can be seen at the site standing around bloodied bodies.
A Syrian government statement said eight people were killed, including a man, his four children and a woman.
However, local officials said seven men were killed and two other people were wounded.
An Associated Press journalist at the funerals in the village's cemetery on Monday saw the bodies of seven men - none of them apparently minors. The discrepancy could not immediately be explained.
Syria's foreign minister Walid al-Moallem said on Monday the attack was "criminal and terrorist aggression," and he warned of retaliation if its borders were violated again.
Syrian television broadcasts reactions from locals following the cross-border attack. "What are the sins of these innocent citizens? They didn't do anything, they were at work. This is a brutal attack," one said.
"I condemn and deplore this attack and I think that all the world will be with Syria against this attack," said another.
In response, the Syrian government has ordered that an American school and a U.S. cultural center in Damascus be closed.
The official SANA news agency says the decision came at a Cabinet meeting Tuesday chaired by Prime Minister Naji Otari.
The report says the Syrian education minister was given instructed to implement the decision.