The Taliban claimed responsibility for the attack, which they said was carried out by a suicide bomber inside the base.
Zabihullah Mujahid, a spokesman for the insurgent group, said the attack had been planned for four months.
The Taliban's spokesman, Zabihullah Mujahid, said Saturday's attack, which he said had been planned for four months, had caused heavy casualties, killing 23 Americans and wounding 44. The movement often exaggerates the number of casualties caused by its operations, Reuters reports.
The Taliban regularly fire rockets at Bagram from outside its perimeter.
Abdul Wahid Sediqqi, spokesman for the governor of Parwan province, where the airfield is based, told The Associated Press he had reports of four dead and around 18 wounded in the attack.
Labourers employed at the base usually line up at the gates around dawn, he said, adding that an attacker could have been among the men entering the base on Saturday.
Investigation shows Taliban suicide bomber dressed as a labourer blew himself up at the NATO air base at Bagram north of the Afghan capital Kabul.
There was no immediate word on the nationalities of those killed and wounded. It is NATO policy not to release such details until families have been informed.
An earlier statement from NATO's Resolute Support mission said the blast happened around 0530 (0100 GMT) and that "force protection and medical teams are responding to the situation.
"It was 05:25 a.m. local time when a powerful explosion took place inside the base. I don't know how many people are killed or wounded but right after the blast happened, all the roads leading to the base were blocked. Now the police don't allow anyone to get close to the base," said Sayed Qasim, a resident of Bagram district.
The attack, which was claimed by the Taliban, underlines the foreign policy challenge that will face U.S. President-elect Donald Trump when he takes office in January.
It follows a suicide attack on the German consulate in the northern city of Mazar-i-Sharif (Mazar-e-Sharif) late on Thursday (November 10) night which killed four people and wounded more than 100 others.
That attack was retaliation for air strikes near the northern city of Kunduz last week which killed more than 30 civilians.
President Barack Obama had originally hoped to have all U.S. forces out of the country by the end of his term but was forced to abandon that aim as Afghan forces struggled to contain the Taliban insurgency.
Under current plans, 8,400 U.S. troops will remain as part of the Resolute Support operation and a separate U.S. counterterrorism mission after Obama decided to slow down a planned reduction of the force, leaving it to his successor to decide future strategy.
12