"The Taliban have taken control of Mazar-e-Sharif," Afzal Hadid told the provincial government, according to Reuters.
He adds that the capital of the Balkh province seems to have fallen without a fight since the security forces with equipment moved towards the border with Uzbekistan.
Sporadic battles are still going on, according to Hadid.
The international force Isaf, which included the Swedish force, was partly stationed in Mazar-e-Sharif.
Afghanistan's second and third largest cities, Kandahar in the south and Herat in the northwest, have also fallen to the Taliban, who have in principle surrounded and isolated Kabul.
The fundamentalist movement has set up camps about 50 km outside the capital, raising fears of an impending offensive.
"Right now, Kabul is not under direct threat, but at the same time it is clear to everyone that the Taliban are trying to isolate the city," John Kirby, spokesman for the US defense headquarters Pentagon, said on Friday.
Approaching Kabul
The Taliban took control of Logar province, just south of the capital, on Saturday, Homa Ahmadi told the Associated Press.
According to Ahmadi, the Taliban have reached a district just 11 kilometers south of Kabul.
Kabul, Jalalabad, Gardez and Khost are currently the only major cities in the country over which the Taliban have not taken control.
President Ashraf Ghani said in a pre-recorded television speech that the re-mobilization of the country's security and defense forces is a top priority.
According to him, "consultations" are underway with local leaders and international partners in the hope of ending the fighting.
Ashraf Ghani also said he would not allow the people to suffer more death and destruction in the wake of the war.
"As your president, my focus is on preventing further instability, violence and forced relocation of my people," Ghani was quoted as saying by Reuters.
Ghani gave no sign of meeting the Taliban's demands for resignation.
Qatar also announces that it has called on the Taliban to cease fire.