KABUL, Afghanistan — A pair of rockets fired by the Taliban struck the United States Embassy in Kabul shortly before dawn on Wednesday, sending hundreds of American diplomats and aid workers based at the mission scrambling into fortified bunkers to start their Christmas Day, the embassy said.

There were no reports of casualties at the embassy. But Afghan officials said that another two rockets hit other parts of the city and that three police officers were wounded when one of the rockets, which had not exploded on impact, detonated as they were trying to defuse it. The other rocket, which did explode on impact, did not cause any casualties or significant damage, said Gen. Zaher Zaher, the police chief of Kabul.

The Taliban quickly claimed responsibility for the attack.

The insurgents said in a statement that they had struck the embassy and the headquarters of the American-led coalition, which is up the road from the mission, with four rockets. “The magnitude of the attack and the scope of the losses have yet to be determined,” the statement said.

That last sentence was a step back from an earlier claim made by Zabiullah Mujahid, a spokesman for the insurgents, who said in a Twitter message posted shortly after the attack that the insurgents had inflicted heavy casualties.