The Gunmen firing on a car killed a local government official and two of his relatives in the country's east on Sunday, officials said.
The attack took place as Abdullah Ahmadzai, a member of Logar province's governing council, was driving into the provincial capital of Puli Alam.
Mr Ahmadzai's brother and cousin were also killed and a bodyguard was injured, said Din Mohammad Darwesh, a spokesman for the provincial government.
Meanwhile, Afghan officials began an investigation into an attack on Saturday in the east that killed 13 policemen.
The two suicide attackers disguised themselves as officers and made it through three security gates before detonating their explosives.
Deputy interior minister Gen Abdul Rahman Rahman led a delegation to paktika province, where the twin blasts struck the police headquarters within 20 minutes of each other, said Zemari Bashary, a spokesman for the interior ministry. Thirteen officers were killed and 14 were wounded, he said.
"The delegation will investigate the incident and find ways to prevent future attacks, not only in paktika but in other provinces in the country," he told reporters at a news conference.
The blasts happened in an area along the Pakistan border that has long been a refuge for Islamist extremists from around the world. It is one of the most violent areas of Afghanistan, where Nato and Afghan forces fight daily against the haqqani network, a Pakistan-based Taliban faction closely tied to Al-Qaida.
The Taliban claimed responsibility in an e-mail sent to the media.
On Sunday Nato said it captured a haqqani leader on November 25 in the eastern Afghan province of Khost. He was accused of carrying out remote-controlled roadside bombings targeting coalition bases and convoys.
The capture brings the number of senior Haqqani leaders captured this month to 20.
Although Nato forces have poured troops into the southern provinces of Kandahar and Helmand and have been making progress in rolling back the Taliban, fighting has continued in the eastern provinces where the haqqani network holds sway.