"This is an attack on Norwegians' security and safety as any other attack would be," said Trine Skei Grande, leader of the Liberal Party which holds nine seats in parliament.
The Norwegian prime minister, justice minister and foreign minister must immediately ascertain what had happened as "we need to know who is supervised and how and why.
Secondly, I expect an apology from the Americans," said Grande.
Knut Arild Hareide, leader of the Christian Democratic Party, said that he was shocked but not surprised by the revelations.
He also urged Prime Minister Erna Solberg to respond to the revelations immediately and to raise the matter with German Chancellor Angela Merkel when they meet on Wednesday.
"We need to know what has happened and how," and Germany and Norway share a common agenda on this issue, said Hareide.
The monitoring scandal has created tensions between Merkel and U.S. President Barack Obama, but so far has not damaged the popular support to transatlantic ties.
Citing a document, the source of which is believed be the whistleblower Edward Snowden, the Norwegian-language newspaper Dagbladet reported in its Tuesday issue that over 33 million Norwegian mobile calls have been monitored by the U.S. National Security Agency (NSA).
The secret service NSA must have watched more than 33 million Norwegian mobile calls for a period of 30 days, according to the secret document, which Dagbladet claims to have access to.
The document is titled "Norway - Last 30 days" and shows that in the period from Dec. 10, 2012 to Jan. 8, 2013, 33,186,042 Norwegian calls have been monitored, about 10 percent of all mobile calls on Norwegian soil
The document is of the type Snowden had previously leaked on surveillance in Germany, France, Spain and Brazil and India.
So far no Norwegian ministers have commented on the latest reports by Norwegian media.