Naqibullah, a doctor at Shiberghan's main hospital, said: "We've got 13 dead and 35 wounded."
Samun confirmed the casualties but said they were caused by the protesters.
He said police had fired into the air to disperse the protesters who had staged an "uprising against the provincial government" and wanted to bring down the government flag and install that of Dostum's faction.
He said: "They were militias of Dostum."
The interior ministry said "tens of gunmen" of Dostum tried to disarm the police and that four police were wounded in the shooting.
The protests came to an end by midday after troops stationed in key government buildings were brought in to help police.
Hamid Karzai, Afghanistan's president, condemned the violence and ordered an immediate investigation.
Putting the death toll at six, the palace quoted Karzai as saying that peaceful protest was the right of every Afghan, but added that it should not involve violence.
The palace said some public and governmental utilities were damaged during the protest.
Dostum, an ethnic Uzbek and a former communist, has been involved in a series of coups and regime changes in nearly three decades of Afghan violence.
He is still officially a military aide to Karzai and considers northern areas as his fiefdom, but his powers have been reduced to a large extent in recent years.
A pro-federalist, Dostum has been accused in the past by several provincial officials in the north of bullying them.
Meanwhile, a suicide attack aimed at US private security contractors in northern Afghanistan killed two Afghan civilians and wounded another, an official said.
Mohammad Ayob Salangi, the provincial police chief, said the bomber detonated explosives strapped to his body as an armoured vehicle from the US firm Dyncorp slowed down at a speed bump in Kunduz city.
The Taliban claimed responsibility for the attack.
Zabihullah Mujahid, a Taliban spokesman, claimed responsibility for the attack and said six soldiers were killed in the blast.
Amar Khail, the deputy provincial police chief, said: "Two civilians were martyred and another civilian was wounded."
The interior ministry confirmed the toll in a statement. Officials said there were no foreign casualties.
A spokesman for German troops stationed in the province with the Nato-led International Security Assistance Force confirmed the suicide blast and said none of its soldiers were involved.