A parliamentary majority including the opposition Social Democrats – but without the populist Danish People's Party – supports Støjberg's law proposal, which would see Denmark refuse 500 UN quota refugees in 2018, a continuation of the country's policy in 2016 and 2017.
Lawmakers in Denmark's parliament began on Tuesday the process of passing a law which would continue the policy of not accepting UN quota refugees.
The proposal has been criticised for adding pressure on countries bordering conflict areas, including Turkey, Jordan and Lebanon, which already accommodate large numbers of refugees.
The UN has encouraged EU countries, including Denmark, to ease the burden on countries such as these by accepting its quota for relocation.
The quota system enables the UN to relocate refugees whose needs cannot be met in countries that neighbour the conflicts they have fled from.
This might include refugees needing special protection, torture victims, unaccompanied women or children with rare illnesses.
Denmark is currently the only UN country currently refusing to accept quota refugees, according to the United Nations High Commissioner for Refugees (UNHCR).
“We have paused [the UN quota refugee programme] because we need to be able to keep up. We simply need breathing space,” Støjberg said on Tuesday.
The minister denied that asylum seeker figures in Denmark, which are now at their lowest lever for nine years, constituted that ‘breathing space'.
“We have a very, very low refugee flow to Denmark. We have not seen a lower number in the last nine years, so there is no doubt that the [immigration] curbs we have introduced have worked,” she said.
“But there are still too few providing for themselves. So that is one of the relevant factors,” she added.
The minister added that the issue of taking in UN quota refugees would be reassessed by the government “year by year”.
She also said that a successor to her post in any future left-wing government would not be able change Denmark's position on quota refugees without first “asking parliament”.
That aspect of the proposal was the basis for the lack of support for the motion from anti-immigration Danish People's Party, said Martin Henriksen, the immigration spokesperson for that party.
“The proposed law leaves a number of interpretations possible,” Henriksen said.
Henriksen's opposite number in the Social Democrats – who voted in favour of Støjberg's proposal not to accommodate quota refugees – said that a future government led by his party could consider reversing the decision.
“A Social Democrat government could well take in quota refugees. That also forms part of the proposal: that any minister can assess it,” Mattias Tesfaye told newspaper Politiken.
Tesfaye added that the extended refusal to take in quota refugees was a “temporary measure, that we have supported this year and next year.”
The MP also told the newspaper that his position was not in conflict with party leader Mette Fredriksen's previous statements confirming that her party would not seek to relax immigration laws should it lead the government after the next election.