Syrian state television said American helicopters raided the village of Sukariya, which lies 550km northeast of Damascus, before flying back towards Iraqi territory.
"Four American helicopters violated Syrian airspace around 4:45pm local time [13:45 GMT] on Sunday," state television and Sana news agency reported.
During the raids, 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," the reports said.
The government said civilians were among the dead, including four children.
"Syria condemns this aggression and holds the American forces responsible for this aggression and all its repercussions"
Syrian government statement
"Syria condemns this aggression and holds the American forces responsible for this aggression and all its repercussions. Syria also calls on the Iraqi government to shoulder its responsibilities and launch and immediate investigation into this serious violation and prevent the use of Iraqi territory for aggression against Syria," a government statement said.
Since the 2003 invasion of Iraq, there have been some instances in which American troops crossed areas of the 600-km border in pursuit of fighters, or aircraft violating Syria's airspace.
But Sunday's raid, if confirmed, would be the first conducted by aircraft and on such a large scale.
Akram Hameed, one of the injured who said he was 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," the man in his 40s 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," he said.
Syria TV 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 alleged attack came just days after the commander of US forces in western Iraq said American troops were redoubling efforts to secure the Syrian border, which he called an "uncontrolled" gateway for fighters entering Iraq.
US Major-General John Kelly said on Thursday that Iraq's western borders with Saudi Arabia and Jordan were fairly tight as a result of good policing by security forces in those countries but that Syria was a "different story".
"The Syrian side is, I guess, uncontrolled by their side," Kelly said. "We still have a certain level of foreign fighter movement."
However, Lieutenant-Colonel Chris Hughes, a spokesman for US forces in western Iraq, said the US division that operates on the Iraqi side of the border was not involved in Sunday's incident.
A Pentagon spokesman in Washington said he had no immediate information on the reported strike but would check further while the White House and CIA declined to comment.
The US and the US-backed Iraqi government frequently say Damascus is not doing enough to stop anti-US fighters, including those from al-Qaeda, from crossing the border into Iraq.
The area targeted by Sunday's raid 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 Shia-led government.
Thabet Salem, a political analyst, told Al Jazeera that the US had appeared to have taken the building workers for infiltrators.
"The Syrian government will be very worried because from the beginning of the Iraq war in 2003 until now, nothing has happened [in Syria]. There have maybe been a few cases, but nothing like eight people killed inside Syria," he said.
"It will raise questions as to why this is happening at this moment - towards the end of the current US administration.
"Syria has deployed large numbers [of security staff] and they have checkpoints every four kilometres along the border. The Syrians have, according to my information, stopped five or six thousand people trying to cross the Syria-Iraq border throughout the last few years."
The raid comes 10 days after Iraqi forces arrested seven Syrian "terrorist" suspects at a checkpoint near the city of Baquba, a base for al-Qaeda fighters, the Iraqi government said.
But last month, Jalal Talabani, Iraq's president, told his US counterpart George Bush that Iran and Syria no longer pose a problem to Iraqi security.
Syria's first ambassador to Iraq in 26 years took up his post in Baghdad this month, bringing more than two decades of discord between the nations to an end.
In September, Condoleezza Rice, the US secretary of state, said she had met Walid Muallem, Syria’s foreign minister, to discuss Middle East peace efforts.
Syrian and American diplomats said the talks touched on Iraq, Lebanon and Middle East peace negotiations.