"We decided to grant Snowden, this figure of international human rights, protection from persecution from the most powerful empire of the world (USA)," Maduro said on Friday in a speech at a parade commemorating Venezuela's July 5 independence day.
Earlier in the day, Nicaraguan President Ortega said he would receive Snowden circumstances permitting.
However, there were no immediate signs that efforts were under way to bring him to either nation.
Washington has revoked the passport of Snowden, who is seeking to evade US justice for leaking details about a vast US electronic surveillance programme to collect phone and Internet data.
Meanwhile, WikiLeaks said yesterday that Snowden has applied to another six countries for asylum.
The 30-year-old is believed to be holed up at a Moscow airport looking for a country that will give him safe haven. Snowden has previously asked 21 countries for asylum.
"Edward Snowden has applied to another six countries for asylum," said the tweet from anti-secrecy website WikiLeaks, which is helping Snowden and has one of its staffers with him in Moscow.
"They will not be named at this time due to attempted US interference."
Snowden can't leave the Moscow airport transit zone without a new travel document.
Snowden's requests for asylum were spurned earlier this week by nations from Switzerland to India. US officials have been contacting countries Snowden might approach for asylum or pass through on the way to a third country to provide reasons why Snowden should be returned to the United States and face charges.
Why Venezuela and Nicaragua?
The offers came one day after leftist South American leaders gathered to denounce the rerouting of Bolivian President Evo Morales' plane over Europe amid reports that the fugitive American was aboard.
Late Venezuelan President Hugo Chavez had maintained a combative relationship with the US and his successor Maduro has continued with anti-US socialist policies.
Venezuela, which holds the largest oil reserves in the world, and the US have gone without ambassadors since 2010. The two countries, however, maintain close energy ties, with Venezuela exporting about a million barrels a day of oil to the US in 2012.
Ortega has had a tenuous relationship with the US since former President Ronald Reagan ordered a trade blockade and funded the Contras rebel group to overthrow him in the 1980s.
(with agencies inputs)