Some unconfirmed reports claim that the Taliban have seized control of the Khamab district headquarters.
The Taliban have yet to comment on the ongoing fierce fighting in the north.
The renewed attacks by the Taliban militants come amid fresh warnings by the group about the need for the US to fully withdraw its forces from Afghanistan after more than a decade and half of occupation.
US President Donald Trump has resisted repeated requests by the Pentagon to approve the deployment of another 4,000-strong US force to Afghanistan, which the US military says is needed to boost the so-called counter-terrorism operations in the country.
There are 8,400 American troops in Afghanistan. Washington claims they are advising and assisting the Afghan military in the fight against the Taliban and Daesh.
Trump is to detail his strategy for the war in Afghanistan, the US’ longest military conflict, in an address later on Monday.
In a prime-time speech to the nation, Trump may announce a modest increase in US troops, as recommended by his senior advisers.
The United States invaded Afghanistan in October 2001 after the September 11 attacks on New York and Washington, and overthrew the Taliban regime. But US forces have remained bogged down there through the presidencies of George W. Bush, Barack Obama and now Trump.