Though no group has claimed responsibility for the abduction of the Indians, Afghan officials have blamed the Taliban.
Daesh claimed responsibility for the first attack on a police station in a heavily Shiite-populated neighbourhood in the city's west, which police spokesman Hashmatullah Estanakzai said had ended.
The second attack took place in front of a police station in Shar-e-Naw neighbourhood in downtown Kabul where a "search and clearing operation" was still under way.
The attack occurred at around 12:30pm when a suicide bomber blew up his explosives near the police headquarters and four others entered into building of a private travel agency in the area and started their attacks from the roof the building, the police chief said.
A senior Afghan security official said intelligence services believe the Haqqani network, a militant group affiliated to the Taliban which has a long record of urban attacks, was the real organizer of the attack.
Public Health Ministry spokesman Wahid Majroh said the toll from Wednesday's attacks is expected to rise as fighting is still underway at one of the police stations.
Each the Taliban and IS incessantly goal Afghanistan's Western-backed authorities and safety forces. It was the deadliest assault on reporters since the fall of the Taliban in 2001.
Kabul police spokesman Hashmat Stanekzai confirmed an explosion near one police station on Wednesday and said a gunbattle was underway there.More news: 'Why Wouldn't We Win?' Donald Trump Celebrates Successful Republican Primaries
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The battle for the compound within the Bilchirgh district, within the northern Faryab province, got here a day after the insurgents captured the district compound within the distant Tala wa Barfak district, within the northern Baghlan province. He says the Taliban also captured several villages nearby.
The Taliban issued a statement saying they control the district and claiming to have killed 10 security forces.
This is just the latest of many attacks that have rocked Afghanistan since mid-April, when registration for the country's October parliamentary elections opened.
Abdul Aziz Beg, head of the governing council within the western Badghis province, mentioned two different troopers have been wounded and one is lacking.
"There are many areas in the province under a high security threat, and this site was one of those areas", he said, adding that the center was some 30 kilometers west of the provincial capital of Qala-e Now.
Earlier this month, an explosion at a mosque in eastern Afghanistan killed at least 14 people and injured dozens more.
The fighting lasted for at least four hours before all attackers were killed, officials said.
After an easing of attacks in Kabul in February and March, Taliban and Daesh have stepped up assaults in the city in recent weeks.