Another 22 were injured when the vehicle blew up about 150 metres from a giant tent which will on Thursday host a meeting of elders on the future of US troops in the country after a NATO coalition pulls out in 2014.
"Inital information shows that unfortunately four civilians, one police and one soldier have been killed in today's attack," Afghan interior ministry spokesman Sediq Sediqqi told AFP.
The Taliban claimed the attack later in the evening. The insurgent group had denounced the assembly, known as a 'Loya Jirga', and warned its members not to participate.
"No doubt the enemy will try its best to target the jirga, but I can say with confidence that our security forces are on high alert and will foil the enemy's desperate effort," said Sediqqi.
According to a statement issued by the interior ministry, the bomber was being pursued by security forces shortly before the explosion.
Nasrullah, a witness, said: "I heard a big bang near the jirga site, and later saw ambulances carrying bloodied people. I saw at least three wounded in army uniforms."
Afghan President Hamid Karzai in a statement condemned the attack, blaming it on the "enemies of peace and progress", a term usually interpreted as a reference to the Taliban insurgents.
Earlier in the day, the president had called on the Taliban and their allies to join the assembly, which is expected to include 2,500 tribal elders and civil leaders from around the country.
The draft Bilateral Security Agreement was hammered out in Kabul last month during a visit by US Secretary of State John Kerry.
But he left without a final deal as Karzai said only a jirga had the authority to decide the contentious issues.
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