The Taliban claimed responsibility for the assault, part of an upswing in violence in the nearly 9-year-old war.
Using light weapons and rocket-propelled grenades, the militants battled international forces for 30 minutes on the outskirts of Jalalabad city, according to information provided by the media office at the airport.
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An Afghan solider and one international service member were wounded in the fighting, NATO said.
"They were not able to breach the perimeter. They were fought off by a combination of Afghan and coalition security forces," German Army Brig. Gen. Josef Blotz, a spokesman for NATO, told reporters at a briefing on Wednesday.
CBS News correspondent Mandy Clark reports June has become the for the U.S. and its allies. Foreign troops are being killed and injured almost daily. In June, at least 100 coalition troops have been killed, including 54 Americans. Almost 400 Americans were wounded.
The air field, shared by Afghans and the international force, is situated on a main road that leads to the Pakistani border
In a text message to The Associated Press in Kabul, Taliban spokesman Zabiullah Mujahid said six suicide attackers killed 32 foreign and Afghan security forces at the airport, about 125 kilometers (78 miles) east of the Afghan capital. The insurgents often claim higher numbers of deaths in their attacks than the official toll.
Elsewhere in the east, U.S. and Afghan forces battled hundreds of militants from an al Qaeda-linked group for a third day Tuesday in Kunar province, the U.S. military said. Two American soldiers were killed Sunday in the first day of the operation.
The attack in Kunar was directed against insurgents believed responsible for the roadside bombing that killed five American service members in the area on June 7, a U.S. statement said.
The militants were believed to be members of the Haqqani group, a faction of the Taliban based in Pakistan that has close ties to al Qaeda. About 600 U.S. and Afghan troops are taking part in the operation, the U.S. statement said.
On Tuesday in Kabul, an Afghan man working for the United Nations was shot and killed in his vehicle near a busy traffic circle.
The Afghan U.N. employee who died was driving a white pickup truck with the blue U.N. logo painted on the side. Another Afghan member of the U.N. staff, who was in the vehicle, was not wounded, the U.N. said.
The morning shooting occurred amid heavy traffic near Massoud circle, an intersection near the U.S. Embassy and an American military base.
"The circumstances of the shooting are not yet clear," a statement released by the U.N. Assistance Mission in Afghanistan said. "United Nations security teams are working with Afghan security institutions to assist investigations."
Blotz said Wednesday that it remains unclear whether the U.N. vehicle was the intended target of the shooting.
U.N. officials extended condolences to the victim, who has not been identified.
"The United Nations condemns violence against any of its personnel under any circumstances," the U.N. statement said. "Those responsible for this killing should be brought to justice without delay."
Also on Tuesday, a roadside bomb wounded seven civilians in Arghistan district of Kandahar and another bomb killed two civilians and wounded two others in Khakrez district, the Afghan Ministry of Interior said.
Afghan and international forces are ramping up security in and around Kandahar, the birthplace of the Taliban.
Blotz said 43 insurgents had been killed or captured in a three-day operation aimed at disrupting insurgents in Panjwai district of Kandahar province, where they have plotted attacks on Kandahar city. In the past two months, joint forces have captured more than 115 suspected insurgents, including more than 15 mid- and senior-level militant leaders, and destroyed four roadside mine factories.