Interior ministry spokesman Nasrat Rahimi said an explosion was heard near the communication ministry around 11:40 am (0710 GMT), followed by sporadic gunfire.
"The information that we have is four attackers have placed themselves near the communication ministry and are engaged in gun battles with the Afghan security forces", Amanduddin Shariati, a security official in Kabul, told AFP news agency. Six people were injured, according to a health ministry spokesman.
In the meantime, the Ministry of Interior in a statement said four civilians and three security personnel lost their lives in the attack and eight other sustained injuries.
There was no immediate word on further casualties and no claim of responsibility for the operation.
The attack occurred a day after talks fell apart between the Taliban and Afghan representatives.
The center of Kabul city witnessed a complex attack by at least four gunmen on Saturday after months of relative calm in the Afghan capital amid accelerating efforts for the peace process.
Live footage on local TV showed government employees fleeing neighbouring Information and Culture Ministry buildings, with some climbing out of windows.
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One security official, who declined to be identified by name, said the initial blast appeared to have been caused by a suicide bomb at the entrance to the ministry.
Both Taliban insurgents and the Islamic State group are active in eastern Afghanistan and have previously claimed attacks in Kabul.
The communication ministry is located in downtown Kabul, about two kilometres (1.25 miles) from the green zone. It is the city's main commercial area and has several large hotels.
The attack followed several months of relative calm in Kabul, which coincided with talks between U.S. and Taliban officials aimed at opening the way for formal peace negotiations to end more than 17 years of war in Afghanistan.
It also comes the week after the Taliban announced its annual spring offensive.
Afghan president Ashraf Ghani strongly condemned the attack in a statement, saying the enemies of Afghanistan, by targeting civil servants, are trying to create terror among the people.