Two U.S. troops died and six Americans were wounded, including four military personnel and two civilians in the attack.
Bagram Air Base, which lies 25 miles (40 kilometers) northeast of Kabul, is surrounded by high mountains and long stretches of desert from which militants could fire rockets. But such attacks, particularly lethal ones, are relatively rare.
Two U.S. troops died and six Americans were wounded, including four military personnel and two civilians, said Lt. Cmdr. Christine Sidenstricker, a U.S. military spokeswoman.
The top government official in Bagram, Kabir Ahmad, said several rockets were fired at the base early Sunday. A spokesman with NATO's International Security Assistance Force said that three rounds landed inside Bagram and one landed outside. He spoke on condition of anonymity because he wasn't the office's top spokesman.
The wounded personnel were taken to the main hospital on Bagram for treatment. ISAF said it wasn't known if any Afghan civilians living near the base were harmed in the attack.
It wasn't immediately clear if New York Times reporter David S. Rohde was at Bagram on Sunday when the rockets hit.
Rohde escaped from kidnappers in Pakistan on Friday after more than seven months in captivity and was flown to Bagram on Saturday. Embassy officials then gave him an emergency passport and FBI officials were guarding him, a U.S. official said Sunday on condition of anonymity because he wasn't authorized to release the information.
A Taliban spokesman, Zabiullah Mujahid, claimed responsibility for the rocket attack. Mujahid also said the Taliban had no involvement in the kidnapping of Rohde and didn't know anything about his escape.
In February 2007, a suicide bomb attack outside Bagram killed 23 people while then-Vice President Dick Cheney was at the base. The attacker never tried to penetrate even the first of several U.S.-manned security checkpoints, instead detonating his explosives among a group of Afghan workers outside the base. The Taliban claimed responsibility.
Bagram is a sprawling Soviet-era base that houses thousands of troops, mostly from the 82nd Airborne Division. Most forces there are American, but many other countries also have troops at the base.
Activity at Bagram is high 24 hours a day, with jets and helicopters taking off at all hours. The base has expanded greatly the last several years and sits next to many houses and the village of Bagram itself.
The two deaths bring to at least 80 the number of U.S. forces killed in Afghanistan this year, a record pace. Last year 151 troops died in Afghanistan.
President Barack Obama ordered 21,000 additional troops to the country this year to fight an increasingly violent Taliban insurgency. There are now about 56,000 U.S. troops in the country, a record number.