The attackers and at least five Afghans were killed, officials said. Taliban spokesman Zabiullah Mujahid claimed responsibility for the assault.
It was the largest attack on 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 Sunday's attack, two vehicles packed with explosives barreled toward the main gate of the base around 6 a.m. local time. The first vehicle, a four-wheel-drive car, blew up at the gate, said Hazrat Hussain Mashreqiwal, a spokesman for the provincial police chief. Guards started shooting at the second vehicle before it too exploded, he added. It was unclear whether the explosives were detonated by the attackers themselves or by shooting from the guards.
Two Afghan students from a private medical school were caught up in the attack and killed, as were three other Afghans working at the base, Mashreqiwal said. He did not know whether the base workers were private guards, members of the security forces or civilian employees.
Nine attackers took part in the assault in total, he said, three of whom were killed in the suicide blasts and another six gunmen who died in the ensuing fighting that lasted a few hours.
Maj. Martyn Crighton, a spokesman for the international military force in Afghanistan, said that helicopters "were deployed and used."
The NATO military coalition described the attack as a failure.
"We can confirm insurgents, including multiple suicide bombers, attacked Jalalabad Airfield this morning. None of the attackers succeeded in breaching the perimeter," Lt. Col. Hagen Messer, a spokesman for the international military coalition, said in an email.
He said that the fighting had ended by midmorning and that reports showed one member of the Afghan security forces was killed. Several foreign troops were wounded, but Messer did not give any numbers or details.
"The final assessment of what happened this morning is not yet complete, but initial reports indicate there were three suicide bombers," Messer said.
In the south, meanwhile, a NATO service member was killed in an insurgent attack, the international coalition said in a statement. It did not provide further details.