Bagram, which is near Kabul, the capital, is one of the biggest military bases in Afghanistan and mainly holds US troops as well as a detention centre where al-Qaeda-linked fighters and "terror" suspects are held.
Al Jazeera's Hoda Abdel-Hamid, reporting from Bagram, described the attack as "quite brazen and daring".
She said the attack started "about 3am when US guards at Bagram spotted a car and started shooting at it".
"That's when this long gun battle that lasted for about eight hours happened.
"It was very intense [the battle] between 3am and until about daylight.
"[A] Taliban spokesman said that the attackers detonated themselves in front of the main gate and managed to enter the airfield.
"But that is something Nato completely refutes. They do say that rocket and mortars have landed inside the base. Nine soldiers have been wounded [and] none, according to Nato, is in critical condition."
Helicopter gunships hovered about the base as the attack went on.
Wednesday's assault follows the Taliban's announcement that they would launch a spring offensiveagainst the Afghan government and foreign forces in Afghanistan in response to Nato's plans for a military campaign on the group's southern stronghold of Kandahar.
On Tuesday, a suicide car bomber attacked a Nato-led military convoy during rush hour in Kabul,killing at least 18 people and six foreign troops. Five of the troops were Americans and one was Canadian.
The Taliban claimed responsibility for Tuesday's blast, one of the deadliest attacks in Kabul in months.
So far this year, 202 Nato soldiers have died, marking January to mid-May period in the Afghan war the deadliest.
At least 520 Nato troops died in 2009, the deadliest year so far for US-led foreign troops since the 2001 US-led invasion brought down the Taliban regime.
Since summer 2009, one or two Nato soldiers have died on average each day.