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.
Taliban militants in Afghanistan say they are responsible for attacking the house of a member of parliament in Kabul, killing at least five people.