(CNN) -  

At least three people died when a suicide bomb exploded near Afghanistan's Kandahar airfield Thursday, hours after U.S. Defense Secretary Leon Panetta had left the city.

One American was killed and three others were wounded, Panetta said. Two Afghan civilians were killed and 18 others were wounded, said Jawid Faisal, a spokesman for the governor of Kandahar province, in the country's violent southern region.

The attack struck an MRAP, the acronym for a Mine-Resistant Ambush Protected vehicle used by U.S. forces, as it was about to enter the base.

The Taliban claimed responsibility, the group's spokesman Qari Yousuf Ahmadi said in an e-mail CNN obtained. He wrote that a "brave Taliban fighter" carried out the attack. The e-mail did not specify whether the explosion was connected to Panetta's visit.

The defense secretary's delegation was never in danger, said a U.S. official traveling with Panetta.

The bomb went off at about 5 p.m. local time and targeted "a foreign forces convoy,"

Coalition spokesman Lt. Col. Hagen Messer confirmed the bombing, saying International Security Assistance Force investigators were at the scene.

"I don't know at this point if this was in any way linked to our visit," said the U.S. official traveling with Panetta.

Pentagon press secretary George Little confirmed the explosion was a vehicle-borne improvised explosive device, a term used for a car bomb.

Panetta invited Afghan President Harmid Karzai to visit Washington early next year to discuss the volatile security situation. Panetta said Karzai appeared willing to visit but didn't say whether the president accepted the invitation.