AFP journalists heard a series of loud explosions in the heart of the Afghan capital followed by volleys of gunfire that were confirmed by Afghan officials and witnesses.
On Tuesday afternoon, the militants attacked security-forces outposts in the district.
The Taliban said the attack in front of a police station in Shar-e-Naw neighbourhood in downtown Kabul was revenge for an Afghan airstrike on a religious ceremony in a Taliban stronghold in northern Afghanistan on April 2.
"Two wounded people have been brought to Kabul hospitals from the site of second explosion in Shar-e-Naw", health ministry spokesman Waheed Majroh said.
The first blast was near a police station in western Kabul's Dasht-e-Barchi district, at around midday, said police spokesman Hashmat Stanekzai.
General John Nicholson, who leads United States and North Atlantic Treaty Organisation forces in Afghanistan, said previously that protecting Kabul was a priority for foreign troops.
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The first and second attacks were later claimed by ISIS and Taliban respectively.
The militants have also captured Bilchiragh district in the northern Faryab province and Kohistan district in Badakhshan province, inflicting casualties on security forces, according to media reports, besides capturing arms and ammunitions, over the past few days.
Attackers targeted two police stations in the Afghan capital, Kabul, on May 9 killing at least seven people and wounding 20 others, authorities said. It was unclear who was behind the assaults, however the Taliban and an Islamic State affiliate are each lively within the province. He said another explosion occurred near a different police station.
A day earlier, the insurgents had captured the district compound in the remote Tala wa Barfak district, in the northern Baghlan province.
Provincial police spokesman Abdul Karim Yuresh says intense fighting is taking place near the compound, adding it's still in government hands.
The Taliban issued an announcement saying they management the district and claiming to have killed 10 safety forces.