DHAKA, Bangladesh — Bangladesh’s capital city reeled in shock on Sunday as clues began to flood social media about the privileged backgrounds of the half-dozen attackers believed to have butchered 20 patrons of a restaurant during a bloody siege here late last week.

The six attackers were killed when the army stormed the Holey Artisan Bakery to end an 11-hour siege early Saturday.

The police declined to name the young men because nobody had shown up as of Sunday night to identify their bodies, but friends and relatives recognized photographs that were posted on a messaging app by the Islamic State, along with praise for the violence.

The men, all in their late teens or early 20s, were products of Bangladesh’s elite, several having attended one of the country’s top English-medium private schools as well as universities both in the country and abroad.

Among them was the son of a former city leader in the prime minister’s own Awami League, the governing party.

“That’s what we’re absolutely riveted by,” said Kazi Anis Ahmed, a writer and publisher of the daily newspaper The Dhaka Tribune. “That these kids from very affluent families with no material want can still be turned to this kind of ideology, motivated not just to the point of killing but also want to be killed.”

That children of the country’s upper classes appear to have joined militant Islamists in an act of such brutality highlighted the radicalization among the largely moderate Muslim population here, a process that has accelerated in recent years.

The attackers intended to kill foreigners, whom they shot and then hacked with sharp weapons, blaming them for hampering the progress of Islam, one of the hostages later said.

For more than three years now, Islamist militants have murdered atheist bloggers, members of religious minorities and others. The Islamic State and a regional branch of Al Qaeda have claimed responsibility for the killings, although the Bangladeshi government continues to insist that local groups were responsible.

The involvement of the Islamic State appeared increasingly more likely during the latest attack, with the organization not only claiming responsibility but later posting the photographs of the men believed to have carried it out.

Some of the rescued hostages remained in police custody on Sunday evening, including a Bangladeshi couple and their two school-aged children who witnessed the massacre, their relatives said.

The country was in the midst of a two-day mourning period declared by Prime Minister Sheikh Hasina, but in the homes of the young men who had been identified as the attackers on social media, families struggled with grief, shame and disbelief.

On Sunday, the police telephoned Meer Hayet Kabir, an executive with a foreign company in Dhaka, asking him to go to the military hospital morgue to identify a body that was possibly that of his 18-year-old son, Meer Saameh Mubasher.

He said he just could not bear to make the trip.

“How will we arrange a funeral for him in these circumstances?” he asked in an interview in his family’s apartment in a wealthy neighborhood close to the diplomatic district. “Who will come?”

“I will have to apologize to the whole world on behalf of my son,” he said.

Mr. Kabir had already been in close touch with the police since Mr. Mubasher disappeared on Feb 29.

The young man was a student at Scholastica School, one of the top private schools in Dhaka. He left home for a tutorial class, which he did not attend, and never returned.

Mr. Kabir said he had made the rounds of police and security officials in the capital since then, seeking help. He gave them a picture of his son, describing him as quiet and pious, someone who prayed five times a day and frequented the local mosque.

Mr. Kabir’s close relatives believe Mr. Mubasher was radicalized either by people he met at a mosque or in school. “I believe some Islamist group recruited my boy” and brainwashed him, Mr. Kabir said.

At least two other young men who appear in the photographs posted by the Islamic State had also attended the Scholastica School, a senior government official said. The official spoke on the condition of anonymity because he was not authorized to speak about the investigation.

That official said that several of the men pictured had studied in Malaysia, at least one at Monash University, and that at least one other had studied at North South University, a private college in Dhaka where several others convicted in the hacking death of a blogger in 2013 were students.

The families of other attackers had also reported them missing, the official said.

Among them was a son of a former city Awami League official who disappeared at the end of December, said Biplob Kumar Das, deputy commissioner at the Dhaka Metropolitan Police.

Mr. Das said police officers searching for the young man, who was in his early 20s, had linked him with militant groups but had not been able to apprehend him. He confirmed that one of the photographs posted by the Islamic State resembled him.

Mr. Kabir said the family was unaware that Meer Saameh Mubasher was being radicalized, except, in retrospect, for one clue. The young man had liked to play the guitar, his father said, but about three months before his disappearance, he stopped.

When Mr. Kabir asked why, his son replied, “Music is not good,” reflecting an Islamist belief that music and dancing are bad influences.

Until now, he had hoped that Mr. Mubasher would reappear one day soon, like some others who disappear into Islamic groups for a time and then come back.

“How can I believe my kin who has humanitarian qualities can be part of these brutal killings?” he asked.

Gowher Rizvi, an adviser on foreign affairs to Ms. Hasina, said the police continued to believe that local groups were behind the militant attacks, and initial indications are that the restaurant siege was also orchestrated by homegrown militants.

Yet Mr. Rizvi said Bangladesh was also willing to consider whether international groups might be involved, although investigators had not seen evidence of external coordination in the Friday attack or the others of the past three years.

Mr. Kabir was steeling himself to make the dreaded trip to the morgue on Monday morning to confirm whether his son was among the dead attackers.

He had been staring at the pictures of the five young men in red-and-white-checked kaffiyehs, trying to convince himself that Mr. Mubasher was not among them.

While he recognized the chubby cheeks, wide nose and big smile in the picture, Mr. Kabir said, there was also something unfamiliar about it.

“I can tell you my boy was really a good humanitarian soul,” he said. “Such a soul cannot do something cruel like this.”

Julfikar Ali Manik and Geeta Anand

Follow Geeta Anand on Twitter @GOAnand.

Julfikar Ali Manik reported from Dhaka, and Geeta Anand from Mumbai, India.

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