CNN reported 12 people were wounded in what was described as a suicide bombing in Jalalabad. No U.S. troops were killed, a spokesman for NATO-led security forces said.
Authorities said an explosives-laden car blew up near the gate of the facility at the city's airport, The Washington Post reported.
The Taliban claimed responsibility for the attack, saying it was to avenge the burning of copies of Muslim holy books by NATO soldiers, CNN said.
The International Security Assistance Force denied Taliban claims that U.S. and Afghan forces were killed Monday in an attack in Naranghar province, near the Pakistani border, CNN said. An ISAF spokesman said some insurgent casualties were reported in the attack.
The accidental burning of Korans last week at Bagram Air Base has fueled violent protests that have caused the death of at least 25 Afghans and four U.S. personnel.
Two of the Americans were a colonel and a major, shot to death Saturday by an Afghan intelligence worker while working inside the Interior Ministry in Kabul.
Two other American soldiers were killed last week by a man clad in an Afghan army uniform.
The violence has continued despite profuse apologies from the top commander of U.S. forces in Afghanistan and appeals for calm by Karzai.
U.S. President Obama also apologized for the incident.
The Taliban appeared to be taking advantage of the Koran-burning by urging Muslims to come together against the foreign forces in the country, observers said.
The Taliban claimed Monday it poisoned food at a dining facility at Forward Operating Base Torkham, near the Afghanistan-Pakistan border, CNN said
The ISAF confirmed food was poisoned during the weekend but it remained unclear whether it was deliberate and a spokesman said nobody was sickened.
The widening protests have forced NATO to withdraw personnel from Afghan government ministries. Some European countries called for pulling out their civilian advisers.
The protests also are coming at a time when the United States and NATO are making plans to withdraw their combat troops and are handing over the security of Afghanistan to Afghans, planning to complete the process by 2014.
U.S. Ambassador to Afghanistan Ryan Crocker told CNN tensions were running high in the country but said there should be no rush to pull out U.S. troops ahead of schedule.
"This is not the time to decide that we are done here," he said. "We have got to redouble our efforts. We have got to create a situation that al-Qaida is not coming back."
On Sunday, protesters attacked a police office and a U.S. military base in northern Kunduz province, some of them lobbing hand grenades. Seven U.S. personnel, believed to be Special Forces members, were injured.
The New York Times reported despite public statements about the United States remaining committed to the Afghan operation, there was growing concern in the Obama administration and the Pentagon about the troop withdrawals -- since the withdrawal program is closely linked to the training of the Afghan army and police forces.
One senior official told the Times the United States now faces a situation of "almost no margin of error" in achieving even its limited goals in Afghanistan.