A member of the panel told RFE/RL's Afghan Service that evidence is being collected in the northern city of Shebergan.
"We are looking into the scene of the incident," the official said. "We are collecting evidence from the scene. As you see our investigation is going on -- let's see when it will end."
A spokesman for the Taliban, Abdul Latif Hakimi, said the ousted radical Islamic movement was responsible for the attack. Hakimi said it was in retaliation for Dostum's alleged role in the killing of Taliban fighters during the U.S.-led invasion of Afghanistan in late 2001.
Dostum's forces are accused of having allowed hundreds of Taliban prisoners to suffocate to death while being transported in containers following their capture. Dostum has repeatedly denied those charges.
Lutfullah Mashal, an Afghan Interior Ministry spokesman, told AFP yesterday that while Afghan officials were aware of the Taliban's claim of responsibility, investigators must be given time to conclude their work to make any certain conclusion.
In an interview with RFE/RL' s Afghan Service, Dostum blamed the attack on terrorists linked with Al Qaeda.
"I have battled the terrorists firmly and unswervingly, and I'll continue the fight," Dostum said. "They know that the freedom of Afghanistan and the toppling of the terrorists started from the north. Therefore, my prediction is that [the perpetrators] are connected with terrorists groups such as Al-Qaeda."
He added that Al-Qaeda and the Taliban remained a danger to Afghan peace and stability.
Rangin Dadfar Sepanta, a guest lecturer at Kabul University and a professor of politics in Germany at Aachen University, said he believes that Taliban and Al-Qaeda supporters are behind the suicide attack against General Dostum.
"Experience shows in Afghanistan that suicide attacks are usually methods used by the Taliban and Al Qaeda," Sepanta said. "Other opposition forces who fight against each other have not committed suicide attacks in Afghanistan."
Dostum is one of Afghanistan's most powerful and feared warlords. He has been accused of torture, brutality, and political opportunism and has many enemies.
However, Sepanta said he believes the larger aim of the attack, which left some 20 people injured, was to destabilize Afghanistan.
"I think that it is not about revenge; it is more aimed at destabilizing the security situation in Afghanistan and bringing military crisis to the north, especially if we take into consideration the fact that people opposed to Mr. Dostum are also in the North," Sepanta said. "The killing of Dostum can cause insecurity and unrest in the region, and this is the policy the Taliban and Al-Qaeda are following in Afghanistan."
The ethnic Uzbek commander, who placed fourth in recent presidential elections, has been left out of the new Afghan cabinet.
His private army was recently disarmed under a national demobilization program. But Dostum has reportedly been allowed to keep a force of 200 bodyguards.
The suicide attack coincided with the release of a statement attributed to ousted Taliban leader Mullah Mohammad Omar. In the statement, which did not mention Dostum, Omar ruled out reconciliation as long as foreign troops remain in Afghanistan. He also vowed to continue the jihad or holy war against "foreign occupation."
In the wake of the failure of the Taliban to disrupt Afghanistan's first direct presidential elections, some observers have speculated that the movement is on the wane.
Others said the attempt to kill Dostum might have been a bid to show that the Taliban remains a force to be reckoned with.