"We are taking matters into our own hands," he was quoted as saying.
The US military in Iraq said it did not have any information about the incident.
The families of those killed in the raid on Sukariya, which lies close to the town of Abu Kamal, buried their loved ones on Monday.
Syrian state television said four US military helicopters had been involved in Sunday's raid on the village.
"Four American helicopters violated Syrian airspace around 4:45pm local time [13:45 GMT] on Sunday," state television reported.
Two of the helicopters landed and dropped off eight US soldiers, who then entered a house, Syrian media reported.
"American soldiers ... attacked a civilian building under construction and fired at workmen inside, causing eight deaths," state television said.
The government said that those killed were workers.
Akram Hameed, a man in his 40s who said he was injured in the attack while fishing in the Euphrates river, told Syrian television he saw four helicopters coming from the border area under a heavy blanket of fire.
"One of the helicopters landed in an agricultural area and eight members disembarked," Hameed said.
"The firing lasted about 15 minutes and when I tried to leave the area on my motorcycle, I was hit by a bullet in the right arm about 20 metres away."
Syrian television showed what it said was the injured wife of the building's guard, in bed in hospital with a tube in her nose, saying that two helicopters landed and two remained in the air during the attack.
The raid targeted an area used by fighters responsible for cross-border attacks into Iraq, Ali al-Dabbagh, the Iraqi government spokesman, said on Monday.
"The attacked area was the scene of activities of terrorist groups operating from Syria against Iraq," he told the Reuters news agency.
"The latest of these groups ... killed 13 police recruits in an [Iraqi] border village. Iraq had asked Syria to hand over this group which uses Syria as a base for its terrorist activities."
Al-Dabbagh would not say who had carried out the attack.
"Iraq is always seeking distinguished relations with its sister Syria," he said.
"The presence of some anti-Iraq groups in Syria, which are supporting and participating in activities against Iraqis, would hinder improvement of these relations".
The US and the US-backed Iraqi government have on several occasions accused Damascus of not doing enough to stop anti-US fighters, including those from al-Qaeda, crossing the border into Iraq.
After news of Sunday's attack emerged, the Syrian government summoned the senior US and Iraqi envoys to Damascus to protest against the raid, the Syrian Arab news agency (Sana) reported.
A Syrian government statement said: "Syria condemns this aggression and holds the American forces responsible for this aggression and all its repercussions."
The statement also called for the Iraqi government to launch an investigation into the attack.
Reem Haddad, the Syrian information ministry spokesperson, sais that the raid breached a recent accord between Iraq and the US.
"This is a flagrant violation of the new [security] agreement between Iraq and the US," she told Al Jazeera.
"One of the points of that agreement is that they do not attack bordering countries."
Lieutenant-Colonel Chris Hughes, a spokesman for US forces in western Iraq, said that the US division that operates on the Iraqi side of the border was not involved in Sunday's incident.
The area targeted lies close to the Iraqi border city of Qaim, which in the past has been a crossing point for fighters, weapons and money used to fuel the armed Sunni opposition against Iraq's government.