AFP reporters heard a string of loud blasts while police confirmed one explosion and a gunfight close to the heavily-guarded embassy compound.
"Today at one o'clock at Kabul's Abdul Haq roundabout a massive suicide attack on local and foreign intelligence facilities is ongoing," said a spokesman for the insurgent group, Zabiullah Mujahid, in a text message to AFP.
One eyewitness reported that attackers had taken up position in a tall building under construction and were exchanging fire with security forces.
An Afghan National Army installation is nearby, as is a Marriott hotel building site, the witness said.
A spokesman for the NATO-led International Security Assistance Force (ISAF) confirmed the attack.
"There is an ongoing attack in the centre of Kabul," he said.The US Embassy did not immediately have further information.
The Taliban are leading a bloody 10-year insurgency in Afghanistan. There are around 140,000 foreign troops in the country.
US will not be cowed by Kabul attacks: Clinton
Americans will not be cowed and will continue to work in Afghanistan, Secretary of State Hillary Clinton said about the Taliban attack on the US embassy in Kabul.
"The civilians who serve will not be intimidated by this kind of cowardly attack," Clinton said, adding there were no casualties among US personnel "a number of Afghan civilians have been hurt."
The US top diplomat added that "we will be vigilant, but we will be continuing (the work there) with even greater commitment."
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