Armed militants in Afghanistan stormed a key govement security agency in the capital Tuesday moing as part of a coordinated assault, killing at least 28 people and wounding more than 320.

The Taliban claimed responsibility for the attack, which included a suicide car bombing. It appeared to have targeted an agency similar to the U.S. Secret Service, providing personal protection for high-ranking govement officials.

Gen. Abdul Rahman Rahimi, the Kabul police chief, said that at least 28 people were killed in the attack, which began when a suicide car bomber struck near the agency compound's gates.

After the explosion, armed gunmen stormed the compound and waged a prolonged battle with govement security forces.

The U.S. Embassy denounced the attack, calling it a senseless act of violence. It added that it supports the Afghan govement's peace process to end such violence.

Ismail Kawasi, spokesman for the Public Health Ministry, said so far 327 are wounded, including women and children, have been brought to area hospitals. An Interior Ministry statement said that dozens of civilians were killed and wounded in the attack. The casualty figures are expected to rise.

"This was one of the most powerful explosions I have ever heard in my life," said Obaidullah Tarakhail, a police commander who was present when the attack began. Tarakhail said he couldn't see or hear anything for 20 minutes after the initial explosion. "All around was dark and covered with thick smoke and dust," he said.

Dozens of civilian apartment buildings, houses, shops and several govement buildings were damaged by the car bomb blast.

Taliban spokesman Zabihullah Mujahid claimed responsibility for the attack. Taliban insurgents have stepped up their attacks recently since announcing the start of their spring offensive last week.

President Ashraf Ghani issued a statement condemning the attack and saying it, "clearly shows the enemy's defeat in face-to-face battle with Afghan security forces."

The attack in Kabul comes four days after another attack by Taliban insurgents in northe Kunduz province which was repelled by the Afghan security forces.

Officials in Kunduz said that security has improved in the city and that the Taliban were defeated in other parts of the province, but operations were still underway to clear militant fighters from the rest of the province.

The Taliban held Kunduz for three days last year before being driven out by a two-week counteroffensive aided by U.S.-airstrikes. It was their biggest foray into an urban area since 2001.

The Associated Press contributed to this report.