Syrian officials said the four attackers shouted religious slogans and threw a grenade into the yard of the US embassy.
"A terrorist operation targeted the US embassy. Security forces have
brought the situation under control. Three terrorists were killed and one was
wounded," the minister, General Bassam Abdel Majid, said on state television.
Witnesses said that two of the attackers had sought refuge in a nearby building but were pursued and killed by security forces.
A car was earlier intercepted by Syrian security on a road leading to the embassy.
"They started shooting at the car whose passengers responded by throwing grenades out of the windows at the mission and nearby buildings," one witness said.
At least three of the attackers are believed to have been killed and one was wounded.
Witnesses said at least one Syrian guard was killed and a Syrian official told Reuters all US diplomats were safe.
A Syrian who works at the US embassy contacted by The Associated Press by telephone also said there were no US casualties.
"We can confirm reports of an attack on our embassy in Damascus by unknown
assailants. The event appears to be over. Local authorities have responded and
are on the scene," US State Department spokesman Curtis Cooper said.
Relations strained
The embassy is in the Rawda area which also houses vital security installations, the houses of senior Syrian officials and other embassies.
The witnesses said Syrian security forces surrounded the embassy building and sealed off the area.
Britain's ambassador to Syria Peter Ford told CNN that the attack did not appear to be a "major al-Qaeda like operation, but an operation by a small group".
One diplomat said the attack involved mortars. "At around 10 o'clock, several mortars were fired at the US embassy, followed by explosions, two of them loud," the Western diplomat posted in Damascus said.
The incident came just a day after the fifth anniversary of the September 11 attacks on the US.
On Monday, Osama bin Laden's number two Ayman al-Zawahiri warned that the Gulf and Israel would be the next targets of Al-Qaeda, in a video message coinciding with the anniversary of the September 11 strikes.
Relations between Damascus and Washington have been strained over Iraq, Lebanon and Syria's support for militants opposed to the peace process with
Israel. Washington is represented in Syria by a charge d'affaires.