In a parliamentary hearing Thursday, Støjberg admitted that the Ministry of Immigration and Integration had been too slow to adopt a European Court of Human Rights (ECHR) ruling on forced expulsions of seriously ill asylum seekers.
Individuals may have been illegally deported from Denmark despite being seriously ill as a result of the malpractice.
Opposition politicians did not hold back in their criticism of the minister following Thursday's hearing at Copenhagen's Christiansborg parliament.
She was rebuked for placing responsibility on public servants working in her ministry as well as called untrustworthy.
Johanne Schmidt-Nielsen, spokesperson on immigration issues with the left-wing Red-Green Alliance (Enhedslisten) party, said Støjberg was yet to answer several questions over the controversy.
A second parliamentary questioning session is likely, according to news agency Ritzau, despite the minister's admissions of wrongdoing by the authority.
“It is shocking how lightly she takes such a serious issue,” Schmidt-Nielsen said.
“[This is] a case where her ministry has not realised a ruling has been made by the ECHR.
“That is a mistake that can cause deaths,” she added.
“It should be possible to trust that what is going on [in the ministry] is in fact legal. We can no longer do that with Støjberg as minister,” the Red-Green Alliance MP continued.
The immigration ministry is reportedly now searching for the whereabouts of seven deported individuals with a view to reviewing their cases.
Josephine Fock, spokesperson on immigration with the environmentalist Alternative party, also rained down criticism on Støjberg.
“It concerns me that she takes it so lightly and places the blame on her public servants,” Fock said.
“We cannot have a ministry that carries out an illegal practice for 13 months. There must be consequences, but we will have to see what those consequences will be,” she added.
During the hearing on Thursday, Støjberg said her ministry had acted incorrectly in taking more than a year to adjust its processes to comply with the December 2016 ECHR ruling.
“Speaking straight, it took too long [for the ministry] to become aware of the ruling. And it also took too long for the [Danish] interpretation to be put in place,” she said during Thursday's hearing, where she was questioned by fellow MPs.
Prior to the hearing, newspaper Politiken reported that the ECHR ruling was relevant in 11 cases, in which seven have already resulted in persons leaving Denmark or being deported.
The ruling – known as the Paposhvili ruling – did not become known to Støjberg's ministry, which determines cases related to the granting of humanitarian residence, until March 2017, when it was notified by the Ministry of Justice, reports Ritzau.
Denmark's Scandinavian neighbours Norway and Sweden had both already implemented the ruling into their practices by that time, according to previous reports. It was not until last weekend that the Danish immigration ministry announced a four-week freeze on forced expulsions of rejected asylum seekers who are seriously ill while it further assesses the issue.
“In this instance, there was a regrettable course of events, which I as minister am obviously not satisfied with,” Støjberg said at Thursday's hearing, adding that a heavy workload in her ministry was one of the reasons for the breakdown in correct practice.
“It is remarkable that Støjberg has not recognised that she has a responsibility. She's the one in charge, and we know incorrect information was given to parliament in this case,” Fock said.
Denmark's largest opposition party, the Social Democrats, was not amongst the parties that summoned Støjberg to Thursday's consultation.
But the Social Democrat spokesperson for immigration Astrid Krag joined the remaining opposition parties in calling for a follow-up hearing over the issue.