The early Monday explosion comes after six days of deadly protests in Afghanistan over the disposal of Quran copies and other Islamic texts in a burn pit last week at a U.S. military base north of the capital, according to The Associated Press.
American officials have called the incident a mistake and issued a series of apologies. Afghan President Hamid Karzai has urged calm, saying that Afghans should not let the insurgents capitalize on their indignation to spark violence.
An Afghan soldier and two local guards were among the dead, provincial police chief Abdullah Azem Stanikzai told AFP.
The bomber drove up to the gates of the airport -- which serves both civilian and international military aircraft -- shortly after dawn and detonated his explosives in a “very strong” blast, said Nangarhar provincial police spokesman Hazrad Mohammed.
An AP photographer saw at least four destroyed cars at the gates of the airport.
NATO forces spokesman Capt. Justin Brockhoff said that no international forces were killed in the early morning attack and that the installation was not breached by the blast.
The Taliban claimed responsibility for the attack, saying a suicide car bomber had driven up to the airport gate and detonated his explosives as international forces were changing from night to morning guard duty.
“This attack is revenge against those soldiers who burned our Quran,” Taliban spokesman Zabiullah Mujahid said in an email.
More than 30 people have been killed in protests and related attacks since the incident came to light this past Tuesday, including four U.S. soldiers.
On Sunday, demonstrators hurled grenades at a small U.S. base in northern Afghanistan and the ensuing gun battle left two Afghans dead and seven NATO troops injured.
Still, the top U.S. diplomat in Afghanistan said Sunday that the violence would not change Washington’s course.
With few signs of the crisis abating, the U.S. ambassador to Afghanistan said the United States should resist the urge to pull troops out of Afghanistan ahead of schedule.
“Tensions are running very high here. I think we need to let things calm down, return to a more normal atmosphere, and then get on with business,” Ambassador Ryan Crocker told CNN’s “State of the Union” in an interview from Kabul.
“This is not the time to decide that we are done here. We have got to redouble our efforts. We’ve got to create a situation that al Qaeda is not coming back,” he said, according to Reuters.
Under an international agreement, foreign combat forces are due to leave Afghanistan by the end of 2014.
In the most high-profile attack, two military advisers were found dead in their office at the Interior Ministry in the heart of the capital with shots to the back of their heads. The slayings inside one of the city’s most heavily guarded buildings raised doubts about safety as coalition troops continue their withdrawal.
The incident prompted NATO, Britain and France to recall hundreds of international advisers from all Afghan ministries in the capital. The advisers are key to helping improve governance and preparing the country's security forces to take on more responsibility.
A manhunt was under way for the main suspect in the shooting -- an Afghan man who worked as a driver for an office on the same floor as the advisers who were killed, Interior Ministry spokesman Sediq Sediqi said. He did not provide further details about the suspect or his possible motive.
The Taliban claimed that the shooter was one of their sympathizers and that an accomplice had helped him get into the compound to kill the Americans in retaliation for the Quran burnings.
The Pentagon said Sunday that Afghanistan’s defense and interior ministers had cancelled a visit to Washington this week to concentrate on addressing security concerns at home.
U.S. Defense Secretary Leon Panetta “understands why that’s a priority and why they are unable to travel to Washington in the coming days,” Pentagon spokesman George Little said in a statement, according to AFP.
President Barack Obama has apologized for the burning of the Quran copies.
With the 2014 timetable unfolding, pressure is growing for an earlier pullout, especially among Washington’s allies in Europe, where the bloody and expensive war is deeply unpopular.
Similar incidents of desecration of the Quran in the past have also sparked violence, although not as widespread and persistent as the riots and protests over the past week.
Last April, seven foreign U.N. staff were killed when protesters over-ran a base in the northern city of Mazar-i-Sharif after a pastor from a fringe church in the United States deliberately burnt a copy of the Quran.