The fundamentalist Taliban group reportedly entered the northern city of Kunduz on Sunday.
The Taliban's advance on the provincial capital comes after two others fell to the insurgents in the past two days.
What we know so far
Afghan forces and the Taliban were fighting fiercely Sunday in the center of Kunduz, officials and a correspondent for the news agency AFP reported.
"Fierce street-to-street fighting is ongoing in different parts of the city. Some security forces have retreated towards the airport," Amruddin Wali, a member of the Kunduz provincial council, told AFP.
The Taliban are reported to have taken at least a number of key sites and buildings in the city, according to the AFP correspondent and Afghanistan's Tolo news outlet.
The Taliban claimed in a Twitter post that it had seized a large number of armored vehicles, vehicles, weapons and military equipment.
The ministry of defense said government forces were fighting to retake these key sites.
"The commando forces have launched a clearing operation. Some areas, including the national radio and TV buildings, have been cleared of the terrorist Taliban," it said in a statement.
Kunduz has been a perennial target for the Taliban, who briefly overran the city in 2015 and again in 2016 but never managed to hold it for long.
Heavy fighting in Sar-e-Pul
Meanwhile, fighting between the Taliban and Afghan forces in the northern Sar-e-Pul province has reportedly reached the provincial capital on Sunday.
"The Taliban have surrounded an army battalion on the outskirts of the city. All other parts of the city are under Taliban control," Mohammad Hussein Mujahidzada, a member of the Sar-e-Pul provincial council, told news agency AFP.
Fighting was also reported on the outskirts of Herat, in the west, and Lashkar Gah and Kandahar in the south.
Taliban sieze Sheberghan
The fundamentalist Taliban group seized the northern city of Sheberghan on Saturday.
Sheberghan is the capital of Jowzjan Province and is home to Uzbek warlord Abdul Rashid Dostum.
Dostum, who is allied with the United States, said he is calling for reinforcements from the Afghan government.
Kabul-based journalist Franz Marty told DW it's likely that Dostum's forces will wage a "counteroperation" in the coming days.
Taliban fighters helped free prisoners from the city's jail, according to videos on social media.
The deputy governor of Jowzjan, Qader Malia, told the AFP news agency that the city had "unfortunately fallen."
Taliban making rapid territorial gains
The Taliban are ramping up their offensive as the US and NATO allies pull out troops from the country.
Anti-Taliban protesters in recent weeks have shouted "Allahu Akbar" (God is the greatest) to show their support for Afghan security forces in the heavy fighting against the group.
The Taliban captured the provincial capital of Zaranj in southwestern Nimroz province on Friday.
Journalist Ali Latifi, who is also based in Kabul, told DW that the Taliban may be trying to "confuse" Afghan government forces, as the two provincial capitals are located in completely different areas of the country.
"The Taliban are trying to stretch the security forces out as thin and as wide as they possibly can," Latifi said. At the same time, he said it begs the question whether the Taliban can keep up fighting on multiple fronts as well.
Could the fighting spread to Kabul?
In regards to the fighting possibly spreading to the country's capital, Kabul, Latifi said the "fortress city" is more secure than other parts of the country.
"Kabul is where they will put all of their focus and their attention," Latifi said, referring to the Afghan government.
"If they do manage to lose Kabul, then that's obviously the ultimate blow to them. They will do everything they can to hold on to the national capital," he added.
A bomb killed an Afghan Air Force pilot in Kabul on Saturday, with the Taliban claiming responsibility for the attack.
Kamran Bokhari, the director of analytical development at the Washington D.C.-based Newlines Institute think tank, told DW that the war in Afghanistan is "far from over" and asserted the Taliban are by and large "a rural and suburban force."
"They have not yet managed to demonstrate the capability to mount successful assaults against well-defended cities and provincial capitals," Bokhari said of the group.
Complete US pullout expected later this month
President Joe Biden announced in April that he would withdraw all troops from Afghanistan by September 11. The pulllout is now expected to be fully complete by August 31, according to recent statements from the commander-in-chief.
Critics of the withdrawal have warned that the Taliban could possibly take over the entire country and roll back advancements in women's rights.
The US invaded Afghanistan in 2001 in pursuit of al-Qaida, the jihadist group behind the 9/11 terrorist attacks. The Taliban was ousted from power during the invasion, with the US working with NATO allies to train the Afghan security forces.
