The attackers and at least five Afghans were killed in yesterday's attack, officials said. Taliban spokesman Zabiullah Mujahid claimed responsibility.
It was the largest clash at the Jalalabad air base since February, when a suicide car bombing at the gate triggered an explosion that killed nine Afghans, six of them civilians.
In the attack, two vehicles packed with explosives sped towards the main gate of the base at around 6am local time.
Hazrat Hussain Mashreqiwal, a spokesman for the provincial police chief, said the first vehicle blew up at the gate. Guards started shooting at the second vehicle before it too exploded. It was unclear if the explosives were detonated by the attackers or by guards' shooting.
Two Afghan university students and three other Afghan civilians working at the base were killed, Mr Mashreqiwal said. He did not know if the three were private guards, members of the security forces or civilian employees.
Nine attackers took part in the assault in total, he said. Three were killed in the suicide blasts and another six died in the ensuing fighting.
Major Martyn Crighton, a spokesman for the international military force in Afghanistan, said that helicopters "were deployed and used" but it was unclear if they were key to killing the militants.
The Nato military coalition described the attack as a failure.
Lt Col Hagen Messer, a spokesman for the international military coalition, said: "We can confirm insurgents, including multiple suicide bombers, attacked Jalalabad airfield this morning.
"None of the attackers succeeded in breaching the perimeter."
"The final assessment of what happened this morning is not yet complete, but initial reports indicate there were three suicide bombers," he said.