Tone Ims Larssen told Norwegian state broadcaster that party leader Siv Jensen should not satisfy herself with minor concessions when she holds a crisis meeting with Prime Minister Erna Solberg on Monday.
“This case is much to serious to be discussing other issues like lowering taxes or road tolls,” she said. “Zero settlement of refugees in Oslo.”
The Progress Party has been threatening to bring down Norway's government since it on Tuesday announced that it would bring home a Norwegian woman who had joined Islamic State group in Syria, together with her two young children.
The woman is scheduled to arrive at Oslo's Gardermoen airport on Friday evening.
On Thursday, Jensen listed terrorism, security, immigration, taxes, road tolls, and infrastructure development as the six areas where the party is likely to make new demands.
But Solberg on Thursday said that it would not be possible to renegotiate the agreement underlying the coalition.
Progress Party MP Kari Kjønnaas Kjos on Thursday said she and many other party representatives wanted to leave the government over the case.
“The party has been shaken after it became known that the government was going to bring home the IS woman,” she said.
“My wish is we go out of government. I do not see a situation where we we can have such a breakthrough that will continue to sit in government,” she told NRK.