Story highlights The Taliban claim responsibility for the attack

ISAF says four NATO coalition service members have been killed

ISAF did not disclose the nationality of those killed

A Pentagon official says the attack happened at Bagram Air Base

Four Americans were killed during a rocket attack at Bagram Air Base, outside of Kabul, a Pentagon official said Tuesday on the condition of anonymity.

The U.S.-led International Security Assistance Force confirmed that four NATO coalition service members had been killed in an attack but did not disclose the nationality of the casualties or the exact location of the attack.

ISAF said the four were killed in an "attack in eastern Afghanistan."

The Taliban claimed responsibility for the attack, the group said in a statement.

News of the casualties came as NATO-led troops transferred security responsibility to Afghan forces.

Afghan President Hamid Karzai has said he welcomes the U.S. troop withdrawal and insists his army can defend the country against the Taliban.

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"It is exactly our job to deal with it, and we are capable of dealing with it," Karzai told CNN's Christiane Amanpour earlier this year.

Even so, there are concerns about the abilities of Afghan security forces to deal with the Taliban and other militant groups.

The Taliban continue to carry out high-profile attacks in the capital, Kabul, even targeting the Afghan Supreme Court during a suicide attack in June. Another strike targeted a building near Kabul International Airport.

On Tuesday, a suicide bomber attacked the convoy of Haji Mohammad Mohaqiq, a member of parliament, killing three people and wounding 21 others. Three bodyguards were among the injured. Mohaqiq -- a Shiite and an ethnic Hazara -- is a member of Afghanistan's political opposition.

American forces, now at about 66,000, are expected to drop to 32,000 by the end of the year.

The plan is to withdraw all combat troops but keep a residual force in the country to help train Afghan forces and carry out counterterrorism operations when needed.

The size of that force is still being discussed.