Police say insurgents have fired rockets and assault rifles at the buildings, along with other government offices in the Afghan capital.
Five attackers are thought to be involved and at least four civilians have been wounded.
The Taliban said several attackers armed with rocket-propelled grenades, AK-47 machine guns and suicide vests were involved.
At least 10 loud explosions were heard, interspersed with gunfire. Television footage showed a burnt-out van and people running away.
Security officials earlier blocked roads around the US embassy and other buildings after the attack reportedly happened in a nearby square. Read More