The area is near foreign embassies and government offices and the attacks follow twin suicide bombings claimed by "Islamic State" (IS) last week, which killed at least 25 people, including nine journalists who had gone to the scene of the first attack.
What we know so far
There were three loud blasts in rapid succession according to police and Interior Ministry officials.
At least five people were killed and more than six people injured in back-to-back suicide bombings.
Both bombings were followed by a gunbattle.
Officials report a "cleanup operation" is underway.
The Taliban and Islamic State group claimed responsibility for the attacks
Afghanistan's intelligence agency blamed the Taliban's Haqqani Network and Pakistani militant group Lashkar-e-Taiba for both incidents.
Interior Ministry spokesman Najib Danish told AFP, "The second attack happened in front of police precinct 10 in Shar-e-Naw in central Kabul," and added that "two attackers who tried to enter the police compound were shot dead."
An official from a branch of the Afghanistan International Bank who was reached by telephone said, "We can hear the gun shots and we are waiting inside the bank's safe room until the clashes end,"
Number of attacks: Kabul has seen an increase in bombings and other attacks against security forces and civilians since the Taliban announced the beginning of their spring offensive on April 25. Fighting usually picks up in Afghanistan as warmer weather melts the snow in mountain passes, which allows insurgents to move around more easily.
Provinces under fire: Earlier in the day, Taliban fighters captured a second remote district compound in two days. Mohammad Hashim, a member of parliament from the northern Faryab province, said insurgents seized the compound in Bilchirgh district and captured several villages nearby.
Repeated attacks in Afghanistan over the past several months have killed and wounded hundreds of innocent Afghans, and shown the world the fragile and worsening state of security in the conflict-stricken country. The incidents have plunged war-weary Afghan citizens into a state of despair and highlighted the limitations faced by the government in Kabul in ensuring public security.
A long series of attacks
The violent incidents have made Afghanistan once again a staple of international headlines. Outfits like the Taliban and the "Islamic State" (IS) have claimed responsibility for the attacks. The Afghan government is under heavy pressure to restore security and take back territory controlled by a number of insurgent groups, including the Taliban and IS.
Last week, the Taliban announced the start of their annual spring offensive, dismissing an offer of peace talks by President Ashraf Ghani. The militants, fighting to restore their version of strict Islamic law to Afghanistan, said their campaign was a response to a more aggressive US military strategy adopted last year, which aims to force the militants into peace talks.
Trump's Afghanistan policy
US President Donald Trump unveiled a new strategy for Afghanistan last year, vowing to deploy more troops, on top of the 11,000 already in the country, to train and advise Afghan security forces. Trump also pledged to support Afghan troops in their war against the Taliban and maintain American presence in the country for as long as there was a need for it.
Afghan peace process
Despite President Ghani's offer in February for peace talks "without preconditions," the Taliban have shown no interest, dismissing the peace overtures as a "conspiracy." Observers say it is unlikely that the militant group will engage in any negotiations, as they currently have the upper hand on the battleground. The Taliban now control more Afghan districts than at any other time since 2001.
Pakistan has been under pressure from Kabul and Washington to stop offering safe havens to militants blamed for attacks in Afghanistan, a charge Islamabad denies and insists that its influence over the insurgents has been exaggerated. Kabul and Islamabad regularly trade accusations of harboring the other country's militants and the harsh language has underscored the strains between them.
Role of the warlords
Apart from the Taliban, Afghan warlords exercise massive influence in the country. Last year, Hizb-i-Islami leader Gulbuddin Hekmatyar returned to Kabul after a 20-year exile to play an active role in Afghan politics. In September 2016, the Afghan government signed a deal with Hekmatyar in the hope that other warlords and militant groups would seek better ties with Kabul.
An inefficient government
In the midst of an endless battle for power, President Ghani's approval ratings continue to plummet. Rampant corruption in the Afghan government and a long tug-of-war within the US-brokered national unity government has had a negative impact on the government's efforts to eradicate terrorism.