Støjberg is facing increased pressure over an illegal parliamentary order to separate asylum seeking couples.
The minister was grilled in a parliamentary consultation last week over an illegal directive to force asylum seeker couples—including individuals under 18 years of age—to live separately, regardless of whether the couples had children.
The directive, issued by Støjberg in February 2016, may have been given despite her prior knowledge that it was illegal to do so, according to reports.
The Social Liberal party has accused Støjberg of lying repeatedly over the issue, reports news agency Ritzau.
Rasmussen's government and its parliamentary allies must ask themselves whether they believe Støjberg should be allowed to continue as minister for immigration, Social Liberal leader Sofie Carsten Nielsen told Ritzau.
Sections of Ministry of Immigration documentation made public by the Politiken newspaper on Wednesday showed that administrative errors were also made in connection with the directive, piling further pressure on the immigration minister.
“There have not just been mistakes. Illegal actions and administration have taken place. That is in direct contradiction of what Inger Støjberg said at the hearing on June 1st,” Nielsen told Ritzau.
“She spoke untruths at the hearing, where she also changed her story. That adds a new dimension to the degree of illegalities committed in this case,” she added.
The government and its allies in parliament's conservative bloc have thus far supported Støjberg, who will face a second, currently unscheduled, hearing.
“Loyalty is important in Danish politics, but we have rule of law and a democracy based on fundamental legal principles of obeying the law. The law is the law, and must be obeyed,” Nielsen said.
At the original hearing, which lasted for five hours, Støjberg repeatedly asserted that no administrative illegalities were committed.
The documents shown by Politiken demonstrate that the immigration authority in several cases failed to carry out complete assessments of the couples in question prior to their separations.
According to Danish law, all pairs should have been given a chance to make a case for themselves before they were separated by force.
But this did not happen until months after the directive was issued by Støjberg, nor did it happen until after the issue had been referred to the parliamentary ombudsman, reports Politiken.
“A majority in parliament, the governing parties and not least the prime minister should take this seriously,” said Nielsen.
“Can you have a minister that sends an illegal directive that is subsequently administrated illegally?”, she added.
The minister also said that her party was “looking into” whether it might report Støjberg to the police if the conservative bloc continued to protect her over the issue.