Two civilians died in the attack in Jalalabad, capital of the eastern province of Nangarhar, around 120 km east of Kabul, Xinhua reported citing Tolo News.
There were conflicting reports about the number of casualties.
CNN said three Afghan soldiers were killed when the militants attacked three different points at Forward Operating Base Fenty, near the Jalalabad airfield, according to the NATO-led International Assistance Security Force (ISAF).
Three suicide bombers and six gunmen were killed in the blasts and the firefight that ensued, provincial police spokesman Havrat Hussain Mashriqwal told CNN.
The attack began around 6 am when two suicide bombers rammed their explosives-laden vehicles into separate entrances of the NATO base, sparking a gunfight between the militants and security forces.
At least 14 Afghan soldiers and four civilians were wounded, police told CNN.
NATO helicopters were seen hovering over the area and firing on the attackers, a witness told Xinhua.
The blasts created a plume of grey smoke above the scene.
Taliban spokesman Zabiullah Mujahid claimed responsibility for the attack.
Mujahid said there were two suicide car bombs and a suicide bomber with an explosive belt used in the attack, which he claimed killed at least 20 people.
Afghan officials told BBC eight suicide attackers were involved in the assault, and all were killed.
A NATO spokesman said the assault was a failure because the Taliban did not penetrate the base.
The force of the explosions is reported to have blown out windows a kilometre away, BBC said.
Local residents said helicopters had fired on the insurgents, and the fighting lasted about 20 minutes.
Sunday's attack was the latest in a series to target the base.
In February, nine people were killed and 12 wounded in a suicide bombing at the front gate of the base. Two months later, four suicide bombers wearing burqas tried to launch an attack there, officials said.
NATO, which currently has around 130,000 troops in Afghanistan, is gradually handing security over to Afghan forces ahead of the departure of most combat troops in 2014.
Kabul: At least 14 people, including nine Taliban men, were killed Sunday when militants wearing suicide vests stormed a major NATO base in Afghanistan, media reports said.
First Published: Sunday, December 02, 2012, 08:52