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KABUL, Afghanistan—At least 10 people, including six coalition force members, were killed and almost 50 wounded when a suicide car bomb targeted a U.S. military convoy outside an Afghan military-recruitment center in Kabul Tuesday morning, police officials said.

A spokesman from the North Atlantic Treaty Organization said six “international service members were killed and several wounded” in the attack, but wouldn’t reveal their nationalities.

Gen. Khalil Dastyar, the deputy police chief of Kabul, said the dead NATO members were American. The Associated Press reported that five of them were U.S. troops; the nationality of the sixth wasn’t immediately disclosed.

A Taliban spokesman, Zabihullah Mujahid, claimed responsibility for the attack, saying that a car loaded with 1,200 pounds of explosives rammed into a U.S. convoy at about 8:30 a.m. local time.

The blast destroyed at least 12 civilian vehicles, one of them a civilian bus; its charred remains were left resting near the road. NATO said five of its vehicles were damaged.

The bomber targeted a small convoy of U.S. military vehicles that were moving along the road near the recruitment center, officials said. The road also skirts a U.S. military base, Camp Julien, that hosts a counterinsurgency training academy for both Afghan and U.S. military personnel.

“Today’s attack was part of the Al Fatah operation and we will continue attacking foreigners and government security forces and their associates,” Mr. Mujahid said.

Earlier this month the Taliban announced the launch of a new spring offensive called “Al Fatah,” Arabic for “to conquer” or “victory.” The Taliban said the offensive would besiege Afghanistan’s major cities and target the diplomats and infrastructure of both the Afghan government and NATO. The Taliban’s ability to strike in the nation’s capital underscores the insurgents’ potency as coalition forces seek to oust them from the southern city of Marjah and are gearing up for a campaign to secure the southern city of Kandahar, the Taliban’s heartland.

The death toll from Tuesday’s attack could rise. Afghan Interior Ministry spokesman Zemarai Bashary said the “death toll is unclear” because officials are still checking hospitals.

He noted that it had been several weeks since the last attack in the capital.

Mohammad Zama, 65 years old, was at work in his shop along the road when he heard a deafening boom. When he stepped outside into the street, “I saw dust and a column of smoke rising from one end of the road,” he said.

“I rushed to the sight and when I got there I saw dead bodies and injured everywhere,” he said. “Among the dead I saw some women in burqas and some children.”

Mr. Zama said two American vehicles, a bus and a few other small civilian cars were charred by the blast. A U.S. helicopter arrived and took away the bodies of the American soldiers, while civilians were taken to a nearby hospital, he said.

—Maria Abi-Habib contributed to this article. Write to Alan Cullison at alan.cullison@wsj.com