The Norwegian PEN Society said on Wednesday that although they could not officially petition the government to review the case, they requested that Justice Minister Grete Faremo look at the possibility of opening an asylum case to determine whether Snowden needs protection.
The NTB news agency subsequently reported that the justice ministry had promised an official response to the letter by Thursday.
"The practice uncovered (by Snowden) in the United States is in clear conflict with the principles of a democratic constitutional state," PEN said on its website.
"It also clearly differs from statements made by the Norwegian government after the July 22nd terror attacks, where the answer was "more democracy, more openness," the letter continued, referencing the acts of Norwegian terrorist Anders Behring Breivik two years ago.
"The United States has, after the September 11th, 2001 attacks, accepted an expansion of its security policy that currently appears to be beyond control, as well as contrary to the values the country was originally founded on," the statement continued.
"The fear of surveillance has already led to significant restrictions on freedom of expression and self-censorship, both in the United States and numerous other countries.
The statement concluded by stating that Norwegian PEN believed Snowden had a well-founded reason to fear how he would be treated in the US, where he to be extradited there.