KABUL—With a new government in place and uncontested control over the country, Afghanistan’s Taliban rulers are clamoring for international recognition of their reinstated Islamic Emirate of Afghanistan.

Nearly a month after the fall of the Afghan republic, no nation has granted such recognition so far. Yet, governments world-wide, as well as the United Nations, are eager to open high-level contacts with the Taliban, especially as the country faces a humanitarian crisis.

Some Western governments say that such dialogue with the Taliban is possible—and desirable—without de jure recognition of their administration. “Before recognition they should have some sort of mandate by the political will of the people,” a senior Western diplomat said. “But apart from the question of recognition we can interact with them, we can engage with them.”

Before the reopening of Western embassies, all closed since the Aug. 15 fall of Kabul, that engagement can take the form of diplomats making short-term visits to Kabul, security conditions on the ground permitting, the diplomat added.

Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani on Sunday became the first foreign government minister to visit Kabul since the Taliban takeover. The conflicting narratives about the brief trip highlighted the group’s desire for international acceptance—and the international community’s reluctance to do so until several conditions are met.

Qatari officials met with officials from the Taliban’s new administration in Kabul on Sunday.

Photo: -/Agence France-Presse/Getty Images

In a triumphant statement, the Taliban implied that their Islamic Emirate of Afghanistan had finally received its first recognition. “The foreign minister of Qatar congratulated the IEA leadership and all Afghan people on the Victory and emphasized boosting bilateral relations,” the Taliban said.

In Doha, there was consternation. The Qatari account of the Kabul talks between Sheikh Mohammed and the Taliban government’s new prime minister, Mullah Mohammad Hassan Akhund, made no mention of any congratulations.

Instead, it reiterated the concerns of much of the international community. In Kabul, the Qatari foreign minister urged the Taliban to form a more inclusive government to ensure freedom of passage for Afghans and foreigners who want to leave the country, and to combat international terrorism, according to the statement from Doha.

A Qatari Foreign Ministry tweet also featured photos of Sheikh Mohammed meeting in Kabul with former Afghan President Hamid Karzai and former chief peace negotiator Abdullah Abdullah. Despite past Taliban promises of sharing power with other political leaders, the Taliban last week formed an interim government that consisted exclusively of the Islamist movement’s senior members.

That government has repeatedly said that it wants Western embassies to return. “The Islamic Emirate of Afghanistan seeks peaceful and positive relations with the world,” proclaims in English the giant billboard that the Taliban have put up on the passenger terminal of Kabul’s international airport.

Sheikh Mohammed also met in Kabul with former Afghan chief peace negotiator Abdullah Abdullah

Photo: -/Agence France-Presse/Getty Images

“Recognition is very important,” Roohullah Umar, a Taliban-affiliated political analyst, said Monday in an interview in the new government’s ministry of information. “If the U.S. and Western nations do not give a hand to Afghanistan, the Taliban will have to stretch their hand to Russia and China.”

Foreign demands for political inclusiveness, he added, make no sense because the Taliban are bound by their commitments to the U.S. in the February 2020 Doha agreements to make sure that Afghan soil won’t be used to endanger the security of other nations.

“The world should realize that what is needed is not inclusivity, but security,” Mr. Umar said. “If we bring into the government Karzai, Abdullah, all these other people who have a relationship with Russia or China or other countries, and they will give someone permission to attack another country, then how can we be held responsible for that?”

The Taliban aren’t a monolithic movement, and many rank-and-file fighters say they are troubled by what they perceive as an unnecessarily soft approach to former enemies. With different factions seeing ministerial positions as spoils of war, the new government reflected above all a desire to contain internal strife, diplomats say.

Taliban slogans have replaced murals of women activists, street vendors started selling the Islamic Emirate's flag, and protests broke out for several days in a row. WSJ's Yaroslav Trofimov looks at Kabul's rapid transformation after the fall of the republic. Photo Composite: Michelle Inez Simon The Wall Street Journal Interactive Edition

On Monday, the Taliban tamped down rumors that Mullah Abdul Ghani Baradar, the relatively moderate deputy prime minister who headed the group’s political office in Doha, was assassinated in clashes Sunday in Kabul’s presidential palace. Mr. Baradar, who was flown back to Afghanistan by a Qatari military plane last month, wasn’t among the notables who met Qatar’s foreign minister Sunday.

In an audio statement published by the Taliban, Mr. Baradar said he was traveling outside Kabul and that reports of his demise were “shameful lies.” Taliban social-media accounts later released footage purporting to be of Mr. Baradar visiting a rural district of Ghazni province.

When the Taliban ruled Kabul between 1996 and 2001, before the U.S. invasion, only Pakistan, Saudi Arabia and the United Arab Emirates granted their regime diplomatic recognition. The previous mujahedeen government—with strongholds in the mountains of northeastern Afghanistan—retained the country’s U.N. seat and other embassies. The Taliban administration liaised with the U.N. and the U.S. through an informal office in Queens, New York.

Taliban officials in Kabul point out that the situation is completely different now. After seizing the capital of the last holdout province, Panjshir, last week, the Taliban now are in uncontested control of the entire country. “After 43 years, the war is finally finished in Afghanistan,” said Enamullah Samangani, a spokesman for the Taliban and former insurgent commander for the northern Samangan province.

There hasn’t been any serious attempt to create an Afghan government in exile since President Ashraf Ghani fled to the U.A.E. on Aug. 15. Yet, for now, all of Afghanistan’s diplomatic missions abroad, including its mission to the U.N. and embassy in Washington, still fly the flag of the fallen Afghan republic.

The U.S. and all other Western countries have closed down their embassies in Kabul after the Taliban takeover, turning the once bustling Green Zone that used to house thousands of diplomats and contractors into a deserted ghost town where stray dogs run through alleys of concrete blast barriers.

Hoping for recognition, the Taliban are protecting most of these embassies, though some—such as Norway’s mission, located just outside the Green Zone—have been looted by Islamist fighters who also on camera destroyed diplomats’ wine collections. The U.S. and many other countries have temporarily moved their diplomats dealing with Afghanistan to Doha.

By contrast, China, Russia, Qatar, Turkey, Iran, Pakistan and neighboring Central Asian states have all retained their diplomatic presence in Afghanistan, with Qatar in particular playing an outsize role in repairing the Kabul airport and organizing the evacuation of foreign citizens last week. The U.N. has also kept a sizable number of staff at its Kabul headquarters. This month senior U.N. officials have visited Kabul to meet key leaders of the Taliban—to whom the U.N. now refers as “the de-facto authorities.”

Maintaining an embassy in a country doesn’t equal recognition of its government, diplomats say, pointing out that many Western nations have kept their embassies open in Myanmar even though they didn’t recognize the military regime that took power after that country’s February coup.

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com