The group posted footage online of their flag-raising fighters there on Monday.
But resistance fighters said they were still in "all strategic positions" and "continuing to fight."
Their leader called for a "national uprising" against the Taliban.
In an audio recording posted on social media, Ahmad Masood, leader of the Afghan National Resistance Front, blamed the international community for legitimizing the Taliban and giving them military and political confidence.
"Wherever you are, inside or outside the country, I call on you to start a national uprising for the dignity, freedom, and prosperity of our country," he said.
The Taliban took control of the rest of Afghanistan three weeks ago and captured the capital Kabul on 15 August following the collapse of the Western-backed government.
It comes after nearly 20 years of U.S. leadership to invade the Taliban regime.
Panjshir, a rugged mountain valley, has between 150,000 and 200,000 people. It was a center of resistance when Afghanistan was under Soviet occupation in the 1980s and during the former Taliban rule, between 1996 and 2001.
The National Front spokesman said earlier that the Taliban did not receive Panjshir, adding that he "rejects the Taliban's allegations".
"The struggle against the Taliban and its partners will continue until justice and freedom prevail," the group tweeted.
"With this victory, get our country completely out of the quagmire of war," Taliban spokesman Zabihullah Mujahid said in a statement.
The stunning Panjshir Valley is one of Afghanistan's smallest provinces, steeped in the greatest mythology.
Its rugged mountainous terrain -- with its maze of valleys, cracks, and caves -- was its biggest weapon in repelling invaders. The Soviet army couldn't conquer it in the 1980s. The Taliban did not control it in the first round in the 1990s.
So in this battle of conflicting narratives, the Taliban could control the arteries and key public areas of Panjshir, and the scene that only its inhabitants know closely may now be home to the most challenging resistance fighters. But the Taliban's progress, however profound, is of great importance -- both symbolically and strategically. It is a glittering gem in the Taliban's new crown as they embark on the re-establishment of their Islamic emirate.
But resistance leaders, including Ahmed Massoud, son of the legendary leader, and Omarullah Saleh, a vocal critic of the Taliban, will not go quietly into the night.
Since taking power, the Taliban have sought to portray themselves as more tolerant, but brutal incidents and repression continue to be reported in parts of Afghanistan.
Although the movement has promised to respect women's rights, many fear a return to the way they were treated when the Taliban were in power before. Women were forced to cover their faces abroad and suffered severe penalties for minor abuses.
Witnesses told the BBC that Taliban gunmen shot and killed pregnant policewoman Pano Najjar on Saturday.
The Taliban told the BBC they were not involved in Nagar's death and were investigating the incident.
Several protests were also held to demand respect for women's rights throughout Afghanistan.
On Monday, a group of women demonstrating in the northern city of Mazar-i-Sharif told the BBC Persian that Taliban fighters had threatened them.
"They swore at us and insulted us and said we should disperse quickly or they would beat us to death," she said, adding that the gunmen also threatened anyone who tried to film them.
Human rights groups have also documented reprisal killings, detention, and persecution of religious minorities. The Taliban have officially said they will not seek revenge on those who worked for the previous government.
So far, the Taliban have not announced the final nature of their new regime.
Spokesman Zabihullah Mujahid told reporters On Monday morning that all-important decisions had already been taken and were now working on "technical issues."
He also said an interim government would be announced first, allowing for changes at a later date.
Later Monday, a White House reporter asked U.S. President Joe Biden whether he would recognize the Taliban government. "This is far from over," he said.
Meanwhile, US Secretary of State Anthony Blinken traveled to Qatar on Tuesday for talks with the government on the situation in Afghanistan and thanked them for their role in helping the US evacuations from Kabul.
More than 120,000 people were airlifted from the Afghan capital in a U.S.-led operation before their troops withdrew completely from the country on August 31.
A State Department official accompanying Mr. Blinken said Monday that the United States had helped evacuate four of its citizens by road, the first US citizen to help the government leave the country since the withdrawal.
The official said the Taliban were aware of the evacuation, but there were no details of their identity or the country from which they crossed from Afghanistan.
U.S. Republican Congressman Ronnie Jackson tweeted after announcing that the four evacuees came from his Texas district.
After 2 weeks & multiple life threatening attempts, I am overjoyed to share that 4 U.S. citizens from #TX13 were part of the first successful ground evacuation since the U.S. left Kabul. Thank you to Cory Mills & the other patriots on his team for saving these BRAVE Americans! pic.twitter.com/1Tv9KRUgcE— Ronny Jackson (@RepRonnyJackson) September 6, 2021