In Nicaragua, Ortega said he was willing to make the same offer "if circumstances allow it." Ortega didn't say what the right circumstances would be when he spoke during a speech in Managua.
He said that the Nicaraguan embassy in Moscow received Snowden's application for asylum and that it was studying the request.
"We have the sovereign right to help a person who felt remorse after finding out how the United States was using technology to spy on the whole world, and especially its European allies," Ortega said.
The offers came amid the ongoing flap about the rerouting of Bolivian President Evo Morales' plane in Europe earlier this week amid reports that Snowden might have been aboard.
Spain said Friday that it had been warned along with other European countries that Snowden, a former U.S. intelligence worker, was aboard the Bolivian presidential plane, an acknowledgement that the manhunt for the fugitive leaker had something to do with the plane's unexpected diversion to Austria.
President Obama has publicly displayed a relaxed attitude toward Snowden's movements, saying last month that he wouldn't be "scrambling jets to get a 29-year-old hacker."
But the drama surrounding the flight of President Morales suggests that pressure is being applied behind the scenes.
Meanwhile, secret-spilling website WikiLeaks said that Snowden, who is still believed to be stuck in a Moscow airport's transit area, had put in asylum applications to six new countries.
The organization said in a message posted Friday to Twitter that it wouldn't be identifying the countries involved "due to attempted U.S. interference."
A number of countries have already rejected asylum applications from Snowden.