The bombing during morning rush hour was one of the worst attacks in Kabul this year.
The explosives-packed car detonated at a security checkpoint outside police headquarters in a neighborhood in western Kabul, police spokesman Firdaus Faramarz said. The Taliban said they had targeted a recruitment center for security forces.
Ninety-two of the wounded were civilians, Deputy Interior Minister Khoshal Sadat told reporters. Four police officers were among those killed, he said.
The attack took place as many Kabul residents were preparing for the Muslim holiday Eid al-Adha. A large plume of smoke rose over the city. Some nearby buildings were left in rubble. Shopkeepers later swept up broken glass.
"I was having breakfast in a restaurant when the explosion happened," said Mohammad Qasem. As windows shattered, he and others rushed into the busy street.
Even as the US-Taliban peace talks continue and the Taliban say they will do more to protect civilians, a growing number of them are being killed. July saw the highest number of civilian casualties in a single month since 2017, with more than 1,500 killed or wounded as attacks spiked, the United Nations said earlier this month.
Any Taliban attack is a barrier to the peace process, presidential spokesman Sediq Seddiqi told reporters, vowing that "Afghan security forces are strong and can protect the Afghan population."
President Ashraf Ghani's government said such attacks apparently are meant to strengthen the Taliban position at the negotiating table but would not succeed.
The Taliban now control roughly half of the country and are at their strongest since 2001, when the US-led invasion toppled their government.
Deputy Interior Minister General Khoshal Sadat said 4,769 Taliban terrorists had been killed since they announced their spring offensive in April.
Seddiqi said Afghan security forces are foiling about seven in 10 planned Taliban attacks.
"Their leaders are being targeted and air operations have increased. To retaliate they are attacking civilian places in the cities," Seddiqi said.
On Tuesday the Taliban warned Afghans to boycott the Sept. 28 presidential election and avoid campaign rallies which "could become potential targets." The vote already has been delayed for months over security and organizational concerns.
The Taliban ordered their members to "stand against" the polls, and previous elections have been rocked by frequent attacks by terrorists trying to undermine Afghanistan's fragile democracy.
The Taliban have been staging near-daily attacks against Afghan forces across the country, saying the war will continue as long as US and NATO forces are still in Afghanistan.
Another round of US-Taliban talks continues this week in the Persian Gulf Arab state of Qatar, where the group maintains an office.
Zalmay Khalilzad, the US envoy tasked with finding a peaceful resolution to America's longest war, this week reported "excellent progress" in the talks. A Taliban official said differences had been resolved over the withdrawal of US troops from Afghanistan and the Taliban guarantee that they will cut ties with other militant groups. The US wants to make sure that Afghanistan will not become a launching pad for attacks against it.
Khalilzad has said he is hoping for a final agreement by Sept. 1. But major challenges remain as the Taliban refuse to negotiate with the Kabul government.
AP, AFP and Reuters contributed to this story.