Daniel Ortega of Nicaragua and Nicolas Maduro of Venezuela made their offers during separate speeches in their home countries Friday afternoon. Snowden has asked for asylum in numerous countries, including Nicaragua and Venezuela.
"As head of state, the government of the Bolivarian Republic of Venezuela decided to offer humanitarian asylum to the young American Edward Snowden so that he can live (without) ... persecution from the empire," Maduro said, referring to the United States. He made the offer during a speech marking the anniversary of Venezuela's independence. It was not immediately clear if there were any conditions to Venezuela's offer.
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 the Nicaraguan embassy in Moscow received Snowden's application for asylum and that it is 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 following a flap about the rerouting of Bolivian President Evo Morales' plane in Europe earlier this week amid reports that Snowden might have been aboard.
Spain on Friday said 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.
It is unclear whether the United States, which has told its European allies that it wants Snowden back, warned Madrid about the Bolivian president's plane. U.S. officials will not detail their conversations with European countries, except to say that they have stated the U.S.'s general position that it wants Snowden back.
President Barack 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 Morales, whose plane was abruptly rerouted to Vienna after apparently being denied permission to fly over France, suggests that pressure is being applied behind the scenes.
Spanish Foreign Minister Jose Manuel Garcia-Margallo told Spanish National Television that "they told us that the information was clear, that he was inside."
He did not identify who "they" were and declined to say whether he had been in contact with the U.S. But he said that European countries' decisions were based on the tip. France has since sent a letter of apology to the Bolivian government.
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. He had already sought asylum from more than 20 countries, many of which turned him down.
Wikileaks said in a message posted to Twitter on Friday that it wouldn't be identifying the countries involved "due to attempted U.S. interference."
Icelandic lawmakers introduced a proposal in Parliament on Thursday to grant immediate citizenship to Snowden, but the idea received minimal support.
Associated Press writer Fabiola Sanchez contributed to this report from Caracas, Venezuela.