Two Taliban rockets landed inside the US embassy compound in Kabul early on Wednesday, causing no casualties but underlining Afghanistan's continuing security problems as many foreigners in the capital marked Christmas Day.

Taliban militants, who have been fighting the US-backed government since being ousted from power in 2001, claimed responsibility for the rocket attacks, which included at least one other strike in the city.

Rocket attacks in Kabul have been rare in recent years, but the insurgents have vowed to step up pressure on the US and Afghan authorities before next year's presidential election and the withdrawal of US-led NATO combat forces.

"At approximately 6:40 local time in Kabul, approximately two rounds of indirect fire impacted the US Embassy compound," a statement from the embassy said.

"All Americans are accounted for and no injuries were sustained.

"The Embassy continues to investigate the attack."

Another rocket landed near a hill where former kings and members of the old royal family are buried in a large mausoleum, a spokesman for the National Directorate of Security told AFP.

"One impacted near Maranjan hill, about one mile (1.6 kilometres) from the presidential palace.

There are no reported casualties," Lutfullah Mashal said.

In a text message to AFP, the Taliban claimed to have caused heavy casualties, but the insurgents regularly make exaggerated claims after attacks.

"Today at around 6am four rockets were fired at the US embassy in Kabul. All hit the target (causing) heavy casualties," Taliban spokesman Zabihullah Mujahid said in the message.

AFP