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The explosion occurred during rush hour in the Puli Mahmood Khan neighbourhood of the city, interior ministry spokesman Nasrat Rahimi said.
An AFP reporter said he could hear gunshots shortly after the blast, which sent a plume of smoke into the air above the area.
The neighbourhood is home to some military and government buildings, as well as the Afghan Football Federation and the Afghan Cricket Board.
No group immediately claimed responsibility. Both the Taliban and the so-called Islamic State group are active in Kabul.
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The negotiations have so far centred on four issues — counter-terrorism, the foreign troop presence, an intra-Afghan dialogue and a permanent ceasefire.
A potential deal would see the US agree to withdraw its troops after more than 17 years in Afghanistan, igniting deep concerns among huge swathes of Afghans who fear the militants will return to some semblance of power.
In return the Taliban would guarantee the country never again became a safe haven for violent extremist groups, as happened with Al-Qaeda before the September 11, 2001 attacks.
US officials have previously said they are hoping for a deal before the upcoming Afghan presidential elections, which have already been delayed twice and are now set for September.