Battle for control
He said that Taliban fighters reportedly had moved into villages that traditionally were controlled by Hezb-e-Islami before the clashes began.
Officials said that the fighters were apparently battling for control of several villages where the central government has almost no presence.
Al Jazeera's James Bays, reporting from Kabul, the Afghan capital, said: "There's been fighting in the north of Afghanistan, very near the very top of the country.
"The border province is called Kunduz. In the province just below that - Baghlan - there's a battle going on. That battle is between the Taliban and the group that's normally seen as one of the Taliban's allies - Hezb-e-Islami.
"They've been involved is some fighting in this area. We had this confirmed to Al Jazeera by Hezb-e-Islami commander. They say that their Hezb-e-Islami forces were told to swear allegiance to Mullar Omar [the Taliban leader].
"They say they are allies [and that] they don't take direct orders from the Taliban. And these clashes have been under way, we understand, for more than 24 hours. Government sources are telling us that at least 50 fighters on both sides have been killed."
Violent clashes between anti-government fighters are rare, although various militias have their own agendas and power struggles are relatively common.
The fighting in Baghlan came as Hamid Karzai, the Afghan president, was making an unannounced visit to the southern province of Helmand.
Quoting Dawud Ahmadi, a spokesman for the Helmand province governor, the Reuters news agency reported that a rocket or mortar fell about 4km from where Karzai was to appear.
The the shell did not explode and no one was hurt, the agency said.
Al Jazeera's Bays said Karzai was visiting Marjah on Sunday, weeks after the town in Helmand was wrested from Taliban control in a major offensive by Afghan and Nato forces.
"The president was making his first visit to the town of Marjah and it is then that I was told that one or two rockets landed near the president - not very close though," he said.
"There are no casualties [but] it shows that the Taliban are still active in this area.
"A Taliban spokesman said that Hamid Karzai wasn't the target. He told Al Jazeera that they fired mortars at a group of VIPs in Marjah because they believed that the UK prime minister [Gordon Brown] was visiting Marjah.
"The Taliban thought they were targeting Brown but they ended up targeting the Afghani president."
Brown has been visiting British troops in Afghanistan who are fighting along side Nato and Afghan forces.