Officials say the insurgents, who are calling on Afghan troops "in enemy ranks" to surrender, have burned buildings, closed schools and planted IEDs in the districts they have seized.
The Taliban are pursuing terrorism against their own people instead of negotiations, Afghan officials have said as the Taliban claim partial victory in their offensive against the government.
The Taliban on Wednesday issued a statement, claiming to have secured large areas and inviting those who work for "enemy ranks", referring to the Afghan and US government, to surrender.
"Their claim of providing justice in secured areas is as hypocritical as it is hollow," Shuja Jamal told TRT World. Jamal is the Afghanistan National Security Council's head of international relations and regional cooperation.
Since early May, the Taliban has launched several major offensives targeting government forces and say they have seized over 80 of the country's 421 districts, although many of their claims are disputed by the government and difficult to independently verify.
"They have destroyed infrastructure wherever they have gone .... planting IEDs in roads leading in and out of districts, preventing women and children trying to flee terror," Jamal said.
"How many districts do the Taliban have a permanent presence in? None," said Waheed Omar, the government's Office of Public and Strategic Affairs director general.
"All over Afghanistan, people have risen against them and in support of the ANDSF", Omar told TRT World, referring to the Afghan security forces.
"This shows they have overplayed their hand by pushing terrorism than negotiations now that foreign forces are leaving ... their war is now with the Afghan people who are standing up alongside the ANDSF," Jamal added.
The Taliban has also vowed in their statement to "grant due Islamic rights" to areas falling under the control of the so-called Islamic Emirate.
On Wednesday, the insurgents captured Jani Khel district of Paktia Province early after heavy clashes with Afghan security forces, Taliban and Afghan official sources told TRT World.
"District centre, police headquarters and government buildings are under complete control," a Taliban source said.
Afghanistan’s main crossing with Tajikistan also remains under the Taliban’s control after the insurgent group seized it on Tuesday. The takeover of the border crossing forced at least 134 government forces to leave all check posts and cross the border into Tajikistan to seek safety.
Tuesday's capture of the Shir Khan Bandar, in the far north of Afghanistan, about 50 kilometres (30 miles) from Kunduz city, is the most significant gain for the Taliban since the US began the final stage of its troop withdrawal in May.
Hospital hit in Kunar
Suspected fighters fired a rocket into a hospital on Wednesday, sparking a blaze that caused extensive damage and destroyed Covid-19 vaccines though there were no reports of casualties, government officials said.
“Different types of vaccine, including doses meant to fight polio and Covid-19 were destroyed in the fire,” said Kunar health official Aziz Safai.
Afghanistan has reported 4,366 deaths due to Covid-19 infections and 107,957 cases, as of Wednesday.
Many health officials say the real number of coronavirus infections is likely much higher but many cases are not being detected because of little testing.
The Taliban denied responsibility of the attack on the hospital.
Deborah Lyons told the UN Security Council that the announcement earlier this year that foreign troops would withdraw sent a "seismic tremor" through Afghanistan.
"Those districts that have been taken surround provincial capitals, suggesting that the Taliban are positioning themselves to try and take these capitals once foreign forces are fully withdrawn," Lyons said.
After 20 years, the United States has started to withdraw its remaining 2,500 troops in Afghanistan and aims to be completely out of the country by September 11.
About 7,000 non-US personnel from mainly NATO countries — along with Australia, New Zealand and Georgia — are also planning to leave by that date.
"All of the major trends — politics, security, the peace process, the economy, the humanitarian emergency, and of course Covid — all of these trends are negative or stagnate," Lyons told the 15-member Security Council. "The possible slide toward dire scenarios is undeniable."
US-backed Afghan forces toppled the Taliban from power in late 2001 for refusing to hand over Al Qaeda leader Osama bin Laden after the September 11, 2001 attacks on the United States.