Vanunu, whom Israeli authorities have barred from leaving Israel, sent his application directly to Norwegian Prime Minister Jens Stoltenberg. His first asylum application to Norway in 2004 was rejected.
"We received it yesterday and it has been sent to the Ministry of Labor and Social Inclusion, which will handle it," a spokeswoman for the Norwegian prime minister's office said.
Vanunu was convicted of treason and imprisoned for 18 years after telling a British newspaper in 1986 about his work as a technician at Israel's main atomic reactor, disclosures which cracked the secrecy around the assumed Israeli nuclear arsenal.
He was released from prison in 2004 but has not been allowed to leave Israel. In 2007, Vanunu was sentenced to six months in prison for violating the terms of his parole.
The Norwegian daily Dagsavisen on Friday cited an Israeli diplomat as saying that giving Vanunu asylum would be considered interference in Israel's internal affairs and a "sign of the generally anti-Israeli sentiment in Norway."
Israel neither confirms nor denies having the Middle East's only nuclear weapons under a policy of "strategic ambiguity."
Declared a prisoner of conscience by Amnesty International, Vanunu has been mentioned as a possible recipient of the Nobel Peace Prize, which is granted annually in Oslo. He was nominated in 2004 by Irish Nobel Peace Prize winner Mairead Corrigan.
Vanunu renewed his application to Norway after reports in Norwegian media said that the minister of local government in the previous center-right government overrode the immigration authority in 2004 to reject his application.
Minister of Labor and Social Inclusion Bjoern Haakon Hanssen said on Thursday that asylum cannot be granted to someone who does not reside in Norway and it was "not timely" to consider him for refugee status since he cannot leave Israel.
"This government has on repeated occasions taken up the Vanunu case in international connections, among others, at the foreign minister level," Hanssen said in a statement. "The government has said that we expect Vanunu to be treated with respect for human rights and not subject to violations."
The University of Tromsoe in north Norway granted Vanunu an honorary doctorate in 2000 and its rector said on Thursday he would be willing to give Vanunu a job.
© 2008 Reuters