There were two blasts in quick succession in a crowded area of the city near government buildings as well as a market and a main intersection, defence ministry spokesman Mohammad Radmanesh said.
Troops, police and civilians rushing to help victims of the first explosion were caught in the second, triggered when a suicide bomber blew himself up, officials said.
The casualty total may increase as more information becomes available, Mohammad Ismail Kawousi, a spokesman for the public health ministry, said.
The Taliban, who have stepped up their campaign against the Western-backed government in recent weeks following a brief lull after the death of their former leader, Mullah Akhtar Mansour, claimed responsibility for the attack, which it said killed 58 officers and commanders.
The double bombing came less than two weeks after gunmen attacked the American University in Kabul, killing 13 people.
Government officials have been preparing for a conference in Brussels next month at which foreign donors, concerned about the ability of the Afghan security forces to withstand Taliban violence, are expected to pledge continuing support over coming years.
(Reporting by Mirwais Harooni; Editing by Robert Birsel and John Stonestreet)
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