Assange entered the Ecuadorian Embassy in London Tuesday and British officials said they would arrest him if he leaves the diplomatic compound, Voice of America reported Sunday.
"Ecuador back in 2010 suggested that perhaps I should come to Ecuador and be given residency, so they are sympathetic over a long period of time so we hope that the asylum application will be viewed favorably," Assange said from the embassy during an interview with an Australian radio station.
President Rafael Correa said: "We'll take the time that is necessary because we're dealing with a very serious topic that we take on with absolute responsibility. However, in the meantime, Mr. Assange is in the Ecuadorian Embassy in London and under the protection of the Ecuadorian state."
The whistle-blowing Web site WikiLeaks has published thousands of documents on the Iraq and Afghanistan wars, and it released sensitive U.S. diplomatic cables.
Assange was accused by two WikiLeaks volunteers in Sweden of sexually attacking them in 2010. He denies the allegations.
No charges have been filed but Swedish officials want to question Assange and successfully sought to have him extradited from Britain.
Rosie O'Donnell unveils nearly 50-pound weight loss
Iranian woman stops the execution of son's killer