DUSHANBE, Tajikistan — Two prominent Afghans who do not recognize the Taliban as Afghanistan’s rightful leaders have begun issuing challenges to the militants from a small but strategic pocket of territory that the Taliban do not control, according to an Afghan diplomat and statements by the leaders.

Although it is unclear how many followers are with them or how many arms they have, both men — the vice president in the toppled government and the son of a renowned mujahedeen leader — command respect among many Afghans.

Their demands at the moment, according to the diplomat, Mohammad Zahir Aghbar, who has been serving as the Afghan ambassador to Tajikistan, are relatively contained. If the Taliban want to avoid a fight and take control of the territory they are in — the difficult-to-penetrate Panjshir Valley — they will need to form an inclusive government, rather than try to lead on their own.

The emergence of even a small area of organized resistance to the Taliban raised the possibility of more fighting in the war-ravaged country and at least a future threat of an insurgency against the former insurgents now controlling Kabul.

The vice president in the ousted government, Amrullah Saleh, claimed in a post on Twitter to have the title of president under Afghanistan’s U.S.-brokered 2004 Constitution because he remains on Afghan territory while the elected president, Ashraf Ghani, has fled.

The other prominent holdout in the valley is Ahmad Massoud, the son of the mujahedeen leader Ahmad Shah Massoud, who successfully defended the Panjshir Valley in years of fighting against the Soviet Union in the 1980s and against the Taliban in the 1990s.

Ahmad Shah Massoud’s stature in the anti-Taliban resistance in the 1990s was such that Al Qaeda assassinated him in a bombing two days before the Sept. 11, 2001, attacks — a killing meant to aid Al Qaeda’s hosts in Afghanistan before the strikes in the United States.

The son, Ahmad Massoud, posted a video on Facebook on Wednesday saying he is in the Panjshir Valley and does not intend to leave Afghanistan. “You can see that I’m in Panjshir and with our people. God willingly I will remain here with our people,” Mr. Massoud said in the video.

“People are ready to fight,” Mr. Aghbar, the ambassador and a longtime ally of the Massoud family, said in an interview in Dushanbe, the capital of Tajikistan. The Panjshir Valley is home to ethnic Tajiks who long opposed the Taliban.

Mr. Aghbar, who said he spoke with both holdouts, said that though Taliban units had attacked Mr. Saleh’s convoy as it traveled from Kabul to the valley on Sunday, the Taliban have not tried to enter the mountain gorge, a naturally defensible site. The valley is about 90 miles north of Kabul.

“If the Taliban who are in Doha and Pakistan agree to a settlement accepting what the world is asking for and corresponds to the needs of the Afghan people, we will have peace and stability,” Mr. Aghbar said.

As Kabul’s defenses crumbled on Sunday, Mr. Aghbar said, he spoke by phone with Mr. Saleh and learned of the plan to hold out in the Panjshir Valley. “I asked, ‘What is your decision?’ He said, ‘I will fight.’”

It’s far from clear what outside help might arrive or whether Mr. Saleh’s claim to continuity of government under the Afghan Constitution will gain traction. The Afghan embassy in Tajikistan is aligned with the cause; in the carpeted meeting rooms of the building, off a dusty, taxi-clogged street in Dushanbe, Mr. Ghani’s photographs came down and Mr. Saleh’s went up.

Farnaz Fassihi contributed reporting from New York.