"Snowden contributed to people knowing about what has happened and spurring public debate" on trust in government, which he said was "a fundamental requirement for peace".
"The level of sophistication and depth of surveillance that citizens all over the world are subject to have stunned us, and stirred debate," they wrote in the nomination letter.
They added that Snowden's actions have "led to the reintroduction of trust and transparency as a leading principle in global security policies".
Solhjell, who was environment minister until Norway's left-wing government lost power last year, told AFP that he was aware of Snowden’s reported request for asylum and that it should be handled according to normal procedures.
"This matter has not affected our decision to nominate Snowden for the peace prize," Solhjell said.
The deadline for submitting nominations for the 2014 peace prize is February 1.
Among those elgible to forward nominations are politicians and barristers around the world, as well as university professors from certain disciplines.
In July 2013 a Swedish sociology professor, Stefan Svallfors, nominated Snowden for the Nobel Peace Prize after the deadline had passed but the nomination is still valid for 2014.