The 63-seat parliament late on Thursday voted against the proposal, which had been made by six members of the opposition, including Birgitta Jonsdottir of the Pirate Party and Ogmundur Jonasson, a former interior minister and member of the Left-Green Movement.
In an entry on her blog, Jonsdottir posted a message attributed to Snowden in which he said he had "been left de facto stateless”.
Iceland's centre-right government had already said that Snowden would not be given special treatment, noting that an asylum application would have to be made on Icelandic soil.
Earlier this week, the interior ministry said a fax with an application for asylum that had been sent to Iceland's embassy in Moscow, could not be considered as it was not possible to verify if it had been sent by Snowden.
Similar applications have been sent to 20 other countries.