Ogmundur Jonasson, whose liberal Left-Green Party is backing the proposal along with the Pirate Party and Brighter Future Party, put the issue before the Judicial Affairs Committee, but the idea received minimal support.
Snowden is believed to be stuck in a Moscow airport transit area, seeking asylum from more than a dozen countries.
At one point, he told the Guardian newspaper that he was inclined to seek asylum in a country that shared his values, and that "the nation that most encompasses this is Iceland."
Granting Snowden immediate citizenship would circumvent that issue.
The same tactic helped get eccentric chess master Bobby Fischer to Iceland from Japan in 2005 to escape US prosecution for breaking sanctions imposed on the former Yugoslavia.
Jonasson argued to parliament on Thursday that Snowden "is now being chased and has nowhere to go," according to Icelandic media.
Leaks by Snowden, a former NSA systems analyst, have revealed the NSA's sweeping data collection of US phone records and some Internet traffic, though US intelligence officials have said the programmes are aimed at targeting foreigners and terrorist suspects mostly overseas.
Six members of minority parties were in favour out of Parliament's 63 members.
Snowden has applied for asylum in Venezuela, Bolivia and 18 other countries, according to WikiLeaks, a secret spilling website that has been advising him.
Like Iceland, many European countries on the list including Austria, Finland, Ireland, the Netherlands, Norway, Spain and Switzerland said he would have to make his request on their soil.
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