General Alishah Paktiawal, the Kabul criminal investigation police chief, said the bomber struck a few hundred metres from the parliament building.
"It was a suicide bombing. Four people were killed and four others were injured. The bomber was driving a yellow and white taxi," he said.
He said it was unclear if the bomber was targeting the parliament building.
Meanwhile, more than 100 Taliban fighters seized control of a district headquarters in the southern province of Zabul early on Friday, the provincial governor's spokesman said.
The Nato-led International Security Assistance Force (ISAF), which has tens of thousands of troops in Afghanistan, said it was checking the information.
The "seizure" of the district comes at the same time as a massive offensive launched last month by ISAF and the Afghan army in nearby Helmand province, where fighters have held a small town for nearly two months.
In other news, Hamid Karzai, the president of Afghanistan, said on Friday he had met members of the Taliban movement to bring about reconciliation.
He said at a news conference in his fortified palace in Kabul that Taliban representatives had been regularly meeting government bodies, adding: "I've had some Taliban coming to speak to me as well, so this process has been there for a long time."
"Having security is of no use unless a massive amount of aid is invested into the community"
Justtone, Nottingham, UK
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But he ruled out talks with Mohammad Omar, the Taliban leader and a close ally of al-Qaeda chief Osama bin Laden, or with foreign fighters.
Karzai also ruled out any more deals with the Taliban to free foreigners or Afghans seized by them.
He that he came under pressure from Rome to approve the release of five rebels last month in return for the freedom of a kidnapped Italian journalist.
Since that deal, the Taliban have kidnapped two French aid workers and their three Afghan guides, and also hold the translator of the Italian reporter as well as five health ministry officials.