Scores were injured. The force of the blast destroyed several vehicles, including a school van and a pick-up truck left twisted and blackened, with another vehicle in flames. Paramedics carried away casualties on stretchers.
Saturday's bomb was placed in a Toyota sedan, a security official at the scene said. Flames billowed from the car and parts of it were ripped apart by the blast and scattered along the street.
Glass was blown out of the windows of the Shinozada hospital and a six-storey building opposite.
Read: Taliban bombing kills up to 29 in northern Afghanistan
"Twelve dead bodies and 66 wounded people were taken to several Kabul hospitals," health official Kabir Amiry said. "Some were in a bad condition."
In a statement the Taliban denied it was behind the attack. No group has claimed responsibility.
Minutes after the explosion, British and US soldiers arrived at the scene in armoured vehicles. Several armed security contractors also pulled up and ran to the blast site.
"One Resolute Support contracted civilian was killed in the attack and two others died of wounds," said Brian Tribus, a spokesperson for the US-led NATO mission known as Resolute Support. He did not say what nationalities the dead were.
Security sources said the contractors worked for DynCorp International. The company, which provides training, security and aviation maintenance to the NATO mission and the Afghan military, did not immediately respond to a request for comment.
Read: Spiralling unrest: Up to 35 dead as four blasts rock Kabul
Bombings have increased in the capital since the government and the Taliban in July confirmed that Mullah Omar had died two years ago. Some analysts say the insurgents are trying to show they remain potent.
The Taliban is fighting to overthrow the foreign-backed government, expel foreign forces from Afghanistan and impose a strict interpretation of Islamic law.
The violence has strained ties with neighbor Pakistan, with Afghan President Ashraf Ghani accusing the government there of not doing enough to stop militants planning attacks from training camps he says lie across the border.
Saturday's bomb was placed in a Toyota sedan, a security official at the scene said. Flames billowed from the car and parts of it were ripped apart by the blast and scattered along the street.
Glass was blown out of the windows of the Shinozada hospital and a six-storey building opposite. On its website, the Shinozada is described as Afghanistan's first private hospital.
.@USEmbassyKabul strongly condemns today's terror attack in Kabul that resulted in deaths of three Resolute Support civilians, many Afghans.
— Department of State (@StateDept) August 22, 2015
Our thoughts, prayers are with those who suffered from today's attack in Kabul. The U.S. remains committed to assisting Afghan partners.
— Department of State (@StateDept) August 22, 2015
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