An Interior Ministry spokeswoman said Thursday that bin Laden is appealing the decision, CNN reported. The government must rule on the appeal within 48 hours.
The younger bin Laden asked for asylum after disembarking late Monday from a plane that was flying from Cairo to Morocco by way of Madrid. He filled out the application Tuesday, getting help from a translator.
During the application and appeals process, he remains in a secure area in the airport, the ministry spokeswoman said.
Omar bin Laden is believed to be in his 20s. He is a citizen of Saudi Arabia.
He is married to a British citizen but an asylum request there was also rejected.
Omar bin Laden has publicly called on his father to give up terrorism.