British news agencies have claimed that the Afghan Taliban have also taken control of the Afghan cities of Kunduz and Sar-e-Pul, one of dozens of areas under Taliban control.
British media say the Afghan Taliban advance continues and tensions are mounting.
British media say that on the orders of the US president, fighter jets bombed Jawzjan to stop the Taliban from advancing.
The Afghan Defense Ministry says 572 Afghan Taliban have so far been killed in the operation.
Former Taliban spokesman Zabihullah Mujahid said the Taliban had announced the capture of Sheberghan, the capital of Jawzjan province.
According to media reports, Shiberghan is the second provincial capital to fall to the Taliban.
The day before, the Taliban had seized Zaranj, the provincial capital of the southwestern province of Nimroz.
The Nimroz police had complained that no army had been sent to fight the militants and no new police aid had been provided.