Fighters engaged in battles with government forces in city that was briefly taken by the armed group a year ago.
The Taliban has launched a coordinated assault on the city of Kunduz in Afghanistan, attacking from four directions and entering the city itself, a senior city police official told the Reuters news agency.
Sheer Ali Kamal, commander of the 808 Tandar police zone in Kunduz, said on Monday that the attack began at around midnight (1930 GMT Sunday) and fighting was still going on in and around the city.
"We are putting all our efforts together to push them back," he said.
Military helicopters were flying overhead and gunfire could be heard in the city.
Al Jazeera’s Jennifer Glasse, reporting from the capital, Kabul, said "it will be difficult to dislodge them as we understand that the Taliban have taken position inside civilian homes".
"Police and security forces are having difficulty distinguishing where exactly the fire is coming from.
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"We are hearing from government officials that Taliban actually said they entered Kunduz city because they were unhappy with Afghan Special Forces activities in two different districts in Kunduz, where the Afghan forces have been fighting with the armed group," our correspondent said.
Kunduz, which fell briefly to the Taliban a year ago, has seen repeated bouts of heavy fighting and was previously seriously threatened in April, July and August.
"A massive operation started on Kunduz capital from four directions early this morning," Taliban spokesman Zabihullah Mujahid said in his official Twitter account.
He said the Nawabad area with four checkpoints had been captured and a number of soldiers had been killed. It was not immediately possible to verify the claim.
A Reuters journalist saw at least five Taliban fighters armed with AK-47 assault rifles, machinesguns and rocket-propelled grenades in the city.
The attack comes as the Taliban have stepped up operations in different parts of Afghanistan, including the strategic southern province of Helmand, where they have been threatening the provincial capital of Lashkar Gah.
Our correspondent said that Taliban has also attacked Nawa district in Helmand province in the south, killing its police chief.
"This does seem like a show of force by the Taliban," she said.
The fall of Kunduz last year was one of the most serious blows suffered by the western-backed government in Kabul since the withdrawal of most international troops at the end of 2014.
A Taliban raid on Tarin Kot, the provincial capital of Uruzgan in the south, on September 8 also sparked fears of another collapse like that in Kunduz last year.
Monday’s attack, a day before the start of a major donor conference in Brussels, underlines the precarious security situation in Afghanistan, where government forces are estimated to have control over no more than two thirds of the country.
Afghanistan’s foreign donor countries are expected to approve at the conference maintaining billions of dollars in funding for the government over the next four years.