After that, the area of the attack shots were heard, causing the security forces began in the area of clearing.
The second attack unfolded in the city centre, where a suicide bomber struck the entrance to a police station in order to clear the way for another four bombers.
Members of the security force were said to be among those killed and wounded.
At least six injured were shifted to hospital by rescue teams after the attacks.More news: TRAILER: 'Arrested Development' Season 5
The Taliban and Islamic State group each claimed responsibility for one of the attacks.
The blasts appear to have targeted two separate police stations as part of a coordinated attack, the first such simultaneous attack on multiple districts in recent memory. Security forces began in the area of clearing. He said there was sporadic gunfire after the blast, as a "cleanup operation" was carried out.
The explosion was confirmed by Kabul police spokesman Hashmat Stanekzai confirmed, he said, " A gun battle was under way there".
The Taliban's main spokesman, Zabihullah Mujahid, issued a statement claiming responsibility for the attack, which came around half an hour after an apparently separate incident in the west of the city. "Two policemen also lost their lives and two policemen are wounded", Estanakzai said.
Two police were killed in the attack and two police and a civilian were wounded.More news: Doctors hit Trump's 'war zone' comments on London crime
It was unclear who was behind the attacks, but the Taliban and an Islamic State affiliate are both active in the province.
Interior Minister Wais Barmak said that "special forces were trying to bring the situation under control".
Violence in Afghanistan has surged since the Taliban launched its annual spring offensive, dubbed as "Al Khandaq", two weeks ago.
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. More than a dozen people died and 33 were injured in that attack.More news: Christina Aguilera releases first album in six years Video