Venezuela’s President Nicolas Maduro said his country would give asylum Edward Snowden, who is believed to be holed up in a transit area of Moscow airport.
Meanwhile Nicaraguan President Daniel Ortega said his country would do so “if circumstances permit”.
WikiLeaks said Edward Snowden had applied to six additional countries on Friday.
The whistleblowing website said it would not name the countries “due to attempted US interference”.
Edward Snowden, 30, has already asked 21 countries for asylum, most of whom have turned down his request.
But even if a country accepted the American’s application, getting there could prove difficult as the European airspace could be closed to any aircraft suspected of carrying the fugitive.
Earlier this week, several European countries reportedly refused to allow the Bolivian president’s jet to cross their airspace on its way back from Moscow – apparently because of suspicions that Edward Snowden was on board.
President Nicolas Maduro made his announcement in a speech on Venezuela’s Independence Day.
“As head of state and government of the Bolivarian Republic of Venezuela I have decided to offer humanitarian asylum to the young US citizen Edward Snowden so he can come to the fatherland of Bolivar and Chavez to live away from the imperial North American persecution,” Nicolas Maduro said.
The US wants to prosecute Edward Snowden over the leaking of thousands of classified intelligence documents.
Earlier Daniel Ortega said Nicaragua had received an application at its embassy in Moscow.
“We are open, respectful of the right to asylum, and it is clear that if circumstances permit it, we would receive Snowden with pleasure and give him asylum here in Nicaragua,” Agence France-Presse quoted the Nicaraguan president as saying.
Daniel Ortega was a fierce opponent of the US during his first period as Nicaragua’s president in the 1980s, after the left-wing Sandinista movement came to power.
Bolivia, which had also suggested it might offer Edward Snowden asylum, saw its presidential plane barred from European airspace on Tuesday.
There was speculation Edward Snowden was on the plane carrying Bolivian President Evo Morales back from Russia to La Paz earlier this week.
“Edward Snowden has applied to another six countries for asylum,” tweeted WikiLeaks, which has been helping the former CIA contractor.
“They will not be named at this time due to attempted US interference.”
The US has been blamed for being behind the decision by France, Portugal, Italy and Spain to close its airspace to Bolivia’s president, whose plane was grounded in Austria for 13 hours as a result.
Earlier on Friday, Spain’s foreign minister Jose Manuel Garcia-Margallo admitted he and the other European countries had been told that Edward Snowden was on board – but refused to say who gave out the information.
He denied Spain had closed its airspace to the presidential plane, explaining that the delay in Austria meant the flight permit had expired and needed to be renewed.
His comment is the first official recognition by the European states that the incident with Evo Morales’ plane was connected with the Snowden affair.
It has been widely condemned by President Morales and several other South American nations, who were critical of the US.
Evo Snowden arrived in the Moscow airport from Hong Kong last month.
He revealed himself to be responsible for the leaking of classified US intelligence documents that revealed a vast surveillance programme of phone and web data.
The documents have also led to allegations that both the UK and French intelligence agencies run similarly vast data collection operations, and the US has been eavesdropping on official EU communications.
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