KABUL, Afghanistan — Taliban insurgents fired rocket-propelled grenades and assault rifles at the U.S. Embassy, NATO headquarters and other buildings in the heart of the Afghan capital today in a brazen attack two days after the United States marked the 10th anniversary of the Sept. 11 terror attacks.

The American Embassy and NATO both said no staff were wounded. Afghan officials said at least one Afghan police officer and two insurgents had been killed as gunfire and explosions resounded across the city well into the afternoon.

The surge of violence was a stark reminder of the instability that continues to plague Afghanistan nearly a decade after the U.S. invasion that ousted the Taliban for harboring al-Qaida, which carried out the 9/11 plane hijackings.

It was the third major attack in Kabul since late June, casting fresh doubts on the ability of Afghans to secure their own country as the U.S. and other foreign troops prepare to withdraw in 2014.

The American Embassy is on the edge of the Wazir Akbar Khan area, which is home to a number of other foreign missions.

U.S. Embassy spokeswoman Kerri Hannan said that staff had been ordered to take cover in hardened structures.

She later issued a statement confirming an attack by gunmen firing rocket-propelled grenades and small arms fire.

“We can confirm there are no casualties at this time among embassy personnel,” she said.

NATO also said none of its staff were wounded in the attack. It said the U.S.-led coalition was providing air support to Afghan security forces.