"This is the most important thing for so many of our voters, and for me it is absolutely essential that we get a tightening," Christian Tybring-Gjedde, one of the party's most outspoken figures, told NRK on Monday.
He said that if the Christian Democrat and Liberal Parties continued to refused to back the new centres, Norway's two-party coalition should scrap the cooperation agreement it signed with the other two parties in September.
"We cannot have a minority dictatorship where two sections representing five percent of voters decide the country's future with regard to asylum and immigration," Tybring-Gjedde said. "It is too serious to allow two mini-parties to decide."
Negotiations ended on Monday without an agreement, with the two minority parties arguing that additional closed asylum centres were unnecessary given the spare capacity at the country's existing closed asylum centre at Trandum, near Oslo.
The Liberal and Christian Democrat parties also want some of the 1,320 children who have been refused asylum, but who have been in the country more than three years, to be given an amnesty.
Tybring-Gjedde said he would be willing to accept an amnesty for some asylum children, so long as there is a strong overall reduction in the number of asylum seekers granted residence in the country.
Ann-Magrit Austenå, from the the Norwegian Norwegian Organisation for Asylum Seekers (NOAS), said she believed Tybring-Gjedde's statements were simply part of Progress's negotiating tactics.
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"It's a play to put pressure on the people negotiating," she said. "They need something symbolic that they can use to say 'we have made a stricter asylum policy', but it's not so easy for them to get real changes that the Liberal parties will not see as a possible violation of human rights."
She said that she believed that Progress would not ultimately fail to win the right to build new detention centres.
"I think it's going to be blocked, because there's no capacity problem as such today," she said.