Now the allegations of torture are roiling Belgium's complicated ruling coalition. Some politicians have suggested that the migration secretary, Theo Francken, the leader who invited the Sudanese officials to Belgium, should consider stepping down over his handling of the matter.
"In the past, we have seen ministers . . . resign if they seem to have lied, even if that is not the case," said Wouter Beke, the leader of the political party Christian Democratic and Flemish, which is a member of the ruling coalition, in an interview with Belgian radio. "It's a question of personal ethics," he said.
Francken has said he has no plans to resign after appearing to mislead Parliament by telling lawmakers, incorrectly, after the allegations emerged that no further deportations were planned. He said he has not received any direct information about deportees being tortured, but "if it turns out that they have indeed been tortured, that's a big problem." He has called for a commission to investigate the allegations.
The Belgian effort follows a deal Italy struck this summer with Libya to halt migrant traffic. Rights groups warn that the agreement increases risks of slavery and abuse in Libya. And in 2016, E.U. leaders promised aid and concessions to Turkey to stop the migrant flow to Greece.
The accusations of torture emerged late last month, when Belgium's Het Laatste Nieuws newspaper published interviews with two of the expelled Sudanese men who said they had been beaten after returning to Sudan.
"They picked me up immediately after landing in Sudan, interrogated me for hours and struck my feet with sticks. They only released me two days later," said one of the men according to the Belgian news account, which used a pseudonym for the man because he feared for his security. "I was so scared that I lay in bed at home for three days."
Another man said he was picked up by police and beaten for three hours during an interrogation, in which the officials accused him of being a political enemy.
Through an intermediary, both men declined a request for an interview, saying their communications were being monitored by the Sudanese government and that Sudanese security officials told them after the initial article was published not to speak to journalists.
The collaboration with the Sudanese officials brought representatives of that government, which has been cited for human rights abuses, into the nation that hosts the capital of the European Union. Although Belgian Prime Minister Charles Michel later said the Belgian and Sudanese governments did not sign an agreement formally outlining the terms of the partnership, the Sudanese officials were granted access to detention facilities holding migrants who had been arrested for being in Belgium without the proper documents.
Then the Sudanese officials were offered the chance to question the detainees. Belgian leaders have said that although representatives of the Belgian government were present, an Arabic translator was not always present so Belgian officials could not always understand what was being said.
Lawyers for some of the migrants said the Sudanese officials threatened the detainees they talked to, warning that if they applied for asylum in Belgium, they would be targeted for abuse in Sudan if they returned home. That alleged threat could have served to discourage asylum requests, since half of Sudanese asylum seekers are rejected in Belgium.
Belgian leaders say that the men had the opportunity to present reasons why they should not be deported. Migrant advocates say that it was a rushed process that failed to give the men the individual review guaranteed them under the law.
The Sudanese Embassy in Belgium did not respond to a request for comment.
"This whole story was bound to end in disaster," said Koert Debeuf, the director of the European branch of the Tahrir Institute for Middle East Policy, who stayed in touch with some of the Sudanese men after they were deported and helped publicize the allegations of abuse. "These Sudanese guys are frightened to death."
Rights groups have condemned the collaboration.
"They did a lot of harm to these people for nothing. The disproportion between the goal they have and the harm they have created is enormous," said Alexis Deswaef, the head of the Belgian League of Human Rights who filed a suit to halt the deportations. The Belgian government won the case on appeal, after a judge ruled that the group had no standing to sue.
But Michel, the prime minister, has so far stood behind the actions of his migration secretary.
"The government has been implementing a firm and humane migration policy," he wrote in a post on Facebook this week. "Belgium makes it a point of honor to respect European and international obligations."
A previous version of this story incorrectly identified the name of a think tank, it is the Tahrir Institute for Middle East Policy.