The Panjshir Valley, around 60 miles of mountain terrain in ​​north-central Afghanistan, is the only one of 34 provinces in the country not controlled by the Taliban, and the people of Panjshir have vowed to continue the fight.

Anti-Taliban forces were seen in Panjshir on Wednesday conducting military exercises and patrolling hilltops as attempts to bring the Taliban and people of Panjishir to talks have reportedly failed.

It’s unclear how many, but a number of Afghans have traveled to the region in hopes of sanctuary in what’s become a holdout for rebel fighters and known as a "historical heartland of resistance."

Taliban General Mobin Khan said earlier this month that the Taliban are "trying to resolve the issue through talks, and Panjshir may surrender peacefully -- otherwise, the responsibility for the war lies with the short-sighted."

-ABC News’ Sohel Uddin and Guy Davies

Taliban forces have rallied around the country to celebrate the withdrawal of U.S. ground forces, holding a parade of vehicles in the Kandahar province on Wednesday.

Haji Mohammad Yousaf, the Taliban's governor in Kandahar, and Taliban spokesperson Zabihullah Mujahid spoke to Afghans gathered at the event.

Meanwhile, in Kabul, scenes around an abandoned airport area, where crowds of Afghans civilians once gathered around U.S. troops, showed empty vehicles covered in barbed wire as Taliban fighters have taken control of the airport and its perimeter.

In an interview with “Good Morning Britain” on Wednesday, Taliban spokesperson Dr. Suhail Shaheen said those with the right documents will be allowed to leave Afghanistan, but "urged" them to stay.

-ABC News' Guy Davies

With all U.S. ground troops out of Afghanistan, scenes around Hamid Karzai International Airport in Kabul on Wednesday showed Taliban fighters in Afghan National Army uniforms after the militant group seized the airport, with some firing celebratory gunshots into the air -- a far different picture from the days preceding.

Hours before Biden addressed the nation on Tuesday and firmly defended the U.S. withdrawal from Afghanistan, the Taliban held a mock funeral in Kabul with show caskets draped with U.S., U.K. and French flags to symbolize what it has called the defeat of NATO allies after 20 years.

The Taliban also released a video overnight they say shows their troops flying over the Kandahar province in an Afghan military helicopter as the militant group works to maintain a hold on the country.

A defiant Biden on Tuesday said that he refused to extend a "forever war" and would not be "extending a forever exit." The president on Wednesday is meeting with Ukrainian President Volodymyr Zelenskyy and does not have any Afghanistan-related briefings on his public schedule.

As the U.S. prepared to evacuate from Kabul airport Monday, the World Health Organization flew a plane into the country with desperately needed aid.

On Monday, 12.5 metric tons of urgent medical supplies were flown from WHO's warehouse in Dubai to Mazar-i-Sharif airport -- not to Kabul, because of the "ongoing disruptions" there, according to WHO.

This is the first medical aid plane to land in Afghanistan since the Taliban took control, according to WHO -- and it comes amid a growing need and deteriorating conditions.

"WHO is exploring more options to get further shipments into the country until a reliable humanitarian airbridge to scale-up collective humanitarian effort is established," the UN agency said in a statement.