The attack came a day after a suicide vehicle bomb attack near a NATO convoy in the Afghan capital Kabul, about 50 miles north of the Bagram base, killed five U.S. troops, a Canadian officer and about a dozen Afghan civilians.
A gun battle ensued after the Taliban insurgents launched the assault on the Bagram base, The New York Times reported. Five U.S. soldiers were wounded, the American command said.
CNN, quoting an army spokesman, said a building at the base sustained minor damage. The spokesman described the attack as "ongoing" and said it "included rockets, small arms and grenades."
Bagram spokeswoman Maj. Virginia McCabe said the attack began early in the morning and was continuing in "the vicinity of Bagram," CNN reported.
The New York Times quoted the Taliban as saying four suicide bombers blew themselves up near the gates of the base and claimed 30 insurgents had entered the base. Those claims could not be confirmed but NATO spokesman Lt. Cmdr. Iain Baxter said no insurgent entered the base.
Authorities could not say whether flights had been suspended at the heavily fortified base surrounded by high fences and thick, concrete walls, CNN reported.
The Los Angeles Times reported U.S. officials downplayed the significance of the incident.
"We're always prepared to deal with attacks on our base," spokesman Lt. Col. Clarence Counts said.