The fighters have once again entered Kunduz after attacking from four directions. The armed group also captured the police headquarters in Nawa, a district in southern Afghanistan.
The Taliban mounted two separate assaults on Kunduz city in the north and Nawa district in the south of Afghanistan Sunday night.
In Nawa, located in Helmand province, local media said the Taliban had captured the police headquarters and killed the district police chief, Ahmad Shah Salim. He was central figure who drove the Taliban out of the district when they took over in August.
"There is fighting everywhere, inside the city and on the streets," a Kunduz resident told TRT World.
Kunduz officials said the attack on the city of 300,000 people began at 2am local time and the Taliban entered from four directions. Taliban fighters entered Kunduz on Monday after an overnight co-ordinated attack in an attempt to take over the city.
Afghan National Security Forces (ANSF) launched a counter-offensive which included airstrikes on Taliban strongholds on the outskirts of the city.
The offensive is the armed group's third attempt in a year to seize control of Kunduz and comes as the Kabul government, including President Ashraf Ghani, head to Brussels for a donor conference.
Fazal Mohammad, a Kunduz resident, said the small number of civilians who are on the streets have come under fire as well.
Arsala, another local, said the city has emptied as people take shelter in their homes.
According to Arsala, the roof and top floor of the four-storey building he lives in is being used by Taliban fighters as part of the ongoing fighting against government forces. He and other residents have taken shelter in the basement.
Online footage posted on Taliban social media profiles shows the fighters walking freely along emptied streets. Their white flag could also be seen hanging from the main roundabout, which appeared to be devoid of security forces who usually man police check posts in the area.
The footage comes as local media reported that the fighters have entered "several" areas of the city. Access to the centre of the city would mean the group is now closer to important strategic locations, including the police headquarters, provincial hospital, university and governor's compound.
In September last year, Kunduz became the first major city to fall to the Taliban since the US-led invasion of 2001. It took government forces 15 days to retake the city, which also shares the same name as the province.
Fighting under way in Sedarak, Qahwa Khana and Nawabad and Charkhab on Khanabad side# Kunduz— Ehsan (@ehsan_af) October 3, 2016
The Taliban spokesperson Zabihullah Mujahid confirmed the attack on Kunduz on his Twitter account, calling it a "massive operation".
In a series of tweets on their official account, Resolute Support, the US-backed international coalition, denied reports that the city was under "significant attack," but said their resources, "including air power, are in position and prepared to assist in Kunduz as needed."
Monday's assault comes on the one-year anniversary of a US airstrike on a hospital run by Medicins Sans Frontieres in Kunduz that resulted in at least 42 deaths. The medical charity had to cancel an event meant to mark the anniversary of the strike which left their facility in ruins.
High civilian casualties
The Taliban's focus on major cities has led to high civilian casualties. The United Nations said in the first six months of 2016, 1,601 civilians were killed and 3,565 were injured.
When the Taliban began their so-called "spring offensive" in 2015, the armed group made it clear they would be targeting urban centres. That strategy also included a push into the northern areas of the country. Since then, provincial capitals in the north and south have been at risk of once again falling into their hands.
Explosion in Jowzjan
A bomb placed in a motorbike exploded in a market in the northern province of Jowzjan, killing six people. The impact of the explosion left 35 others, including women and children, injured. All of the dead and injured were civilians.
The provincial governor's office told local media the blast took place in a crowded area of Darzab district.