The attack took place in the compound of the Helmand MP, Mir Wali. He is believed to have survived but two of his grandchildren are reported to have been killed.
Security forces at the scene say the gunmen are now holding hostages.
Security in Kabul has deteriorated significantly throughout 2016.
The three gunmen began their assault early on Wednesday evening, with at least one of the attackers reported by Tolo News to have detonated explosives inside.
It reported that also among the dead were the 25-year-old son of Kandahar MP Obaidullah Barikzai and two security force members.
A number of people are reported to have been wounded including a former police chief. Gunfire and explosions were recently reported to have been heard at the premises in the west of the city.
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Relatives and friends of Mr Wali - who is reported to have escaped the attackers through the house of a neighbour - are believed to be among the hostages.
The Taliban in a statement said suicide bombers attacked the house because it was hosting an "important gathering of security officials".
The attack again exposes continuing instability in Afghanistan, with regular strikes by suicide bombers and gunmen in recent months in Helmand and in Kabul. The city has been targeted repeatedly by the militants throughout this year.
Police special forces have now been deployed at the scene, officials say, and their priority is to evacuate people from the house and surrounding areas.
The Taliban have made sweeping gains in Helmand - a major opium-producing region - since international coalition forces withdrew from Afghanistan in 2014.

Locke was himself sacked by Raith Rovers last month with the Scottish Championship side on a run of 15 games without a victory.
The 41-year-old inherits a side sitting seven points adrift at the foot of Scottish League Two.
Caretakers Neil Hastings and Burton O'Brien take charge for the final time against Berwick Rangers on Saturday.
But Locke will be present as the Blue Brazil look to end a run of 15 games without a win.
Cowdenbeath said in a website statement: "We ask all fans to give Gary a very warm welcome to Central Park and their full support as we face the major challenge that lies ahead in the next couple of months."
The Fife club accepted Fox's resignation as head coach on Monday.
"The club regrets that, despite Liam's great efforts and true professionalism, he was not able to bring the success we all wished for," said Cowdenbeath.
"He did face a number of challenges this season, some of which few managers would normally expect to encounter, especially in their first season in management.
"He leaves Central Park with the respect and best wishes of the chairman and all the directors of the club."
Fox, who had previously been on the coaching staff at Hearts, had taken charge at Central Park during the summer.
The 33-year-old said: "Firstly, I'd like to thank Cowdenbeath for giving me the opportunity to manage their football club.
"The experience gained and lessons learned in a short period of time will no doubt prove invaluable to me in my career."
Locke is also a former Hearts player and started his managerial career at Tynecastle before moving on to Kilmarnock then, last summer, to Stark's Park.
Taliban militants in Afghanistan say they are responsible for attacking the house of a member of parliament in Kabul, killing at least five people.
[NEXT_CONCEPT]
Gary Locke has been appointed manager of Cowdenbeath until the end of the season after the exit of Liam Fox.