"Let's hope it is granted and that in the meantime conditions are established to ensure respect for his rights, as contemplated in all the international treaties," Foreign Minister Ricardo Patino said.
Ecuador was the first country to say it would consider granting Snowden asylum after the 30-year-old former contractor set off a storm by revealing the extent of US electronic spying.
But it later backed away from the offer amid intense US diplomatic pressure. Venezuela, Bolivia and Nicaragua have since said they would give Snowden safe haven.
Snowden, who is wanted in the United States, has applied for temporary asylum in Russia after three weeks of being stranded in a transit zone at Moscow's Sheremetyevo Airport, a Kremlin-linked lawyer told AFP.
Patino said it was fortunate that Venezuela, Bolivia and Nicaragua had offered Snowden asylum because "it lightened the load the Ecuadoran government has taken on in this."
Ecuador is currently sheltering WikiLeaks founder Julian Assange at its embassy in London.