"For many years, the (populist) Progress Party has claimed that more influence should be granted to the citizens," Anundsen, a Progress Party minister was quoted by Norwegian news agency NTB during parliamentary question time.
"This proposition shouldn't shock anybody," he said.
"But within the government coalition, the Progress Party is sticking to our cooperation agreement (with the other right and centre-right parties) and does not plan a referendum on this matter."
The minister's remarks clashed with comments from Per Sandberg, the Progress Party's deputy head, who appeared to throw his weight behind a Swiss-style referendum on immigration.
"It is important to have this debate in this country," Sandberg told Norway's NRK channel.
"The referendum in Switzerland will affect the EU and later also Norway," he said.
"We have been aware of this problem for a long time, and now it is time for this debate to come."
On Tuesday, the immigration spokesman for the Progress Party, which wants to restrict the arrival of immigrants, demanded a referendum similar to the one held last Sunday in Switzerland.
"The idea of a referendum is interesting and Norway should also organize a referendum on immigration," Mazyar Keshvari told Norwegian tabloid Verdens Gang (VG).
"I'm completely certain that a majority wants to tighten up" the policy, he said.
Norway is not a member of the EU but is included in the European Economic Area and the Schengen Area which allow relatively unrestricted movement of citizens.
Referendums in oil-rich Norway are far less common than in Switzerland.
On Sunday, 50.3 percent of the Swiss voters decided to reverse a decision which gave equal footing to European Union citizens in the Swiss labour market.
The European Commission reacted strongly, saying that it would assess EU ties with Switzerland.