The insurgents now control or hold sway over roughly half the country.
Farhad denied the claim, saying Afghan security forces were still in control of the district headquarters. He said that Afghan reinforcements drove the Taliban from the area. "Security situation is under the control right now," he added.
There has been some destruction to the district police chief headquarters, said Farhad.
The district is very remote, said Mohammad Afzel Hadid, head of the Balkh provincial council. He also confirmed that the Taliban were defeated after reinforcements arrived.
The Taliban had casualties during the battle, said Hadid, but he couldn't provide any figure.
In a separate Taliban attack in eastern Ghazni province, at least three civilians were shot and killed by Taliban, said Ahmad Khan Serat, spokesman for the provincial police chief.
He added that six other civilians were wounded when the Taliban targeted the civilian vehicle traveling from Jaghatu district toward Ghazni city.
The Taliban did not immediately comment on the attack in Ghazni.
Despite upgraded security, authorities said 431 polling stations stayed closed because it was impossible to guarantee their security since they were either in areas under Taliban control or in places where insurgents could threaten nearby villages.
Results of the vote are not due for weeks.
The Afghan government was sidelined in the U.S.-Taliban talks, aimed at ending America's longest war. The Taliban have refused to negotiate with Kabul officials as they consider the Afghan government a U.S. puppet.