MOSCOW — Ecuador signaled on Wednesday that it may deliberate slowly on the asylum application from Edward J. Snowden, the fugitive former security contractor wanted in the United States, raising the possibility that he could spend weeks in legal limbo as he plots his next steps inside a Moscow airport transit area.

Ecuador’s approach was conveyed in statements by its foreign minister and from its embassy in Washington as the Obama administration sought to further lighten a cold war atmosphere with Russia, which said Tuesday that it would not extradite Mr. Snowden to face criminal charges in the United States.

Mr. Snowden, 30, whose revelations of American surveillance activities abroad have angered the Obama administration and raised a debate about governmental invasion of privacy, remained out of sight on Wednesday. It was his fourth day in a restricted international transit area of Moscow’s Sheremetyevo airport, as speculation intensified over when he would leave and where he would go.

Ecuador’s foreign minister, Ricardo Patiño, suggested at a news conference in Malaysia that his government could take months to decide whether to grant Mr. Snowden’s asylum request, and that his country’s relations with the United States would figure in that decision.