After taking control of Afghanistan, the Taliban has pledged to be a responsible member of the international community that doesn’t pose a threat to any country’s security.

However, the Islamist movement’s victory in Afghanistan has elevated its most radical and violent branch, the Haqqani network. Having perpetrated some of the deadliest attacks of the 20-year war, the network—unlike the broader Taliban—has been designated as a terrorist organization by the United States since 2012.

Closely linked to al Qaeda, the network has also for decades been involved in the hostage-taking of Westerners, and currently holds at least one American citizen captive, according to U.S. officials.

“I do not believe that anyone in the West fully understands the reach of the Haqqani network,” said retired Lt. Gen. Michael K. Nagata, a former director of strategy for the National Counterterrorism Center. “It is the single most impressive nonstate militant group I have ever seen, with the exception of ISIS in the first two years of the caliphate.”

Experts who have followed the group for years worry that its consolidation of power will enable the kind of transnational terrorism that the U.S.-led invasion of 2001 aimed to eradicate.

Jalaluddin Haqqani, founder of the militant network, in 1998.

Photo: Mohammed Riaz/associated press

Since the Taliban’s takeover of Kabul, the normally elusive Haqqani network, which is built around a family of the same name, has assumed a public role in the Afghan capital. Khalil Haqqani, brother of the group’s founder, Jalaluddin, addressed the faithful in public in Kabul’s Pol-e Khishti Mosque last week—despite a $5 million U.S. bounty on his head.

According to people who attended, Mr. Haqqani said that Afghanistan had been freed, would become peaceful, and that people associated with the ousted U.S-backed government would be forgiven.

Along with his nephew, Anas Haqqani, who spent four years in custody at Bagram air base, Khalil met with former President Hamid Karzai and the fallen republic’s chief peace negotiator Abdullah Abdullah for talks about a more inclusive government that could gain international recognition.

A Taliban delegation led by Anas Haqqani met with former Afghan government officials.

Photo: Agence France-Presse/Getty Images

The network’s de facto leader, Sirajuddin Haqqani, son of Jalaluddin, worked closely with Osama bin Laden’s top lieutenant and al Qaeda fighters in Afghanistan, according to files recovered in bin Laden’s compound in Pakistan. Today, Sirajuddin is the Taliban’s military chief, and his forces have been put in charge of security in Kabul.

“The Haqqanis expose the lie that there is a line between Taliban and other jihadist groups, especially al Qaeda,” said H.R. McMaster, a national security adviser in the Trump administration and former deputy commander for U.S.-led coalition forces in Afghanistan.

The Taliban pledged in the February 2020 Doha agreement with the U.S. that Afghanistan would never again host international terrorist groups like al Qaeda. Mr. Biden has justified the American withdrawal by emphasizing that al Qaeda has been eradicated from Afghanistan.

“We went to Afghanistan for the express purpose of getting rid of al Qaeda in Afghanistan, as well as getting Osama bin Laden. And we did,” President Biden said Friday.

At Kabul airport, where an explosion injured several U.S. marines Thursday evening, prominent Taliban units with ties to the Haqqani network now operate within feet of U.S. troops securing the area to facilitate evacuations of American citizens and some Afghans. Ahead of the attack, U.S. and European officials had warned people not to come to the airport due to an imminent terrorist threat.

Afghan officials have for years accused the Haqqani network of facilitating deadly attacks on civilians by providing Islamic State’s local affiliate with technical assistance and access to criminal networks in Kabul, even though Islamic State and the mainstream Taliban are sworn enemies. Such attacks include an assault by gunmen on a maternity ward in Kabul in May 2020 that killed 24 people, mostly women and children.

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At the airport, Badri 313, an elite Taliban unit, plays a particularly prominent role. They are among the best trained and equipped forces operating within Afghanistan, and the Taliban posted footage of its fighters guarding the airport, wearing sophisticated tactical gear and holding American-acquired weapons—within sight of U.S. Marines.

The Haqqani network has a force called the Badri Army, which some U.S. officials believe is the same as the Badri 313. Intelligence officials of the fallen Afghan republic say the two groups are the same.

Afghan Army Gen. Yasin Zia, who served as chief of staff of the army until June and before than held a senior intelligence role, said the Haqqani network, due to training by the Pakistani intelligence services, is by far the most proficient of Afghan militant groups in surveillance and counter surveillance. Because of that, it is likely to take control of the country’s intelligence apparatus, he said.

Afghan TV showed images of the Taliban's Badri 313 on patrol in the country.

Photo: Agence France-Presse/Getty Images

While the Haqqanis’ connections to Islamic State are disputed by some analysts and officials, the network’s ties to al Qaeda are clear.

“Relations between the Taliban, especially the Haqqani network, and al Qaeda remain close, based on friendship, a history of shared struggle, ideological sympathy and intermarriage,” a May United Nations Security Council report said. The U.N. has stated that between 400 and 600 al Qaeda fighters are active in 12 provinces, and that the group’s leader, Ayman al-Zawahiri, is still based in Afghanistan.

Born out of the CIA-funded anti-Soviet mujahedeen movement in the 1980s, the Haqqani network pledged allegiance to the Taliban in 1995. Since then, the family has been an integral part of the Taliban, but has maintained its autonomy and relations with a host of international jihadist groups, particularly al Qaeda.

Sirajuddin Haqqani also had close relations with a prominent al Qaeda commander, Abdul Rauf Zakir, who was responsible for protecting Osama bin Laden’s son Hamza, according to U.S. intelligence.

“Al Qaeda is in lockstep with the Taliban,” said Rob French, a retired senior analyst with the Afghanistan Threat Finance Cell, a multiagency U.S. intelligence organization. “They are basically a subsidiary of the Taliban at this point.”

Write to Sune Engel Rasmussen at sune.rasmussen@wsj.com and Nancy A. Youssef at nancy.youssef@wsj.com