The Venezuelan president, Nicolas Maduro, and his Nicaraguan counterpart, Daneil Ortega, made the asylum offers on Friday, shortly after they and other Latin American leaders met to denounce the diversion of a plane carrying the Bolivian president, Evo Morales, due to suspicions that Snowden might have been on board.
The invitations came as Snowden sent out new requests for asylum to six countries, in addition to the 20 he has already contacted, according to WikiLeaks, which claims to be in regular contact with the former National Security Agency contractor.
Most of the countries have refused or given technical reasons why an application is not valid, but several Latin American leaders have rallied together with expressions of solidarity and welcome.
"As head of state of the Bolivarian republic of Venezuela, I have decided to offer humanitarian asylum to the young Snowden … to protect this young man from persecution by the empire," said Maduro who, along with his predecessor Hugo Chávez, often refers to the US as "the empire".
The previous day, Maduro told the Telesur TV channel that Venezuela had received an extradition request from the US, which he had already rejected.
A copy of the request, seen by the Guardian, notes that Snowden "unlawfully released classified information and documents to international media outlets" and names the Guardian and the Washington Post. Dated 3 July and sent in English and Spanish, it says: "The United States seeks Snowden's provisional arrest should Snowden seek to travel to or transit through Venezuela. Snowden is a flight risk because of the substantial charges he is facing and his current and active attempts to remain a fugitive."
It adds that he is charged with unauthorised disclosure of national defence information, unauthorised disclosure of classified communication intelligence and theft of government property. Each of these three charges carries a maximum penalty of 10 years imprisonment and a fine of $250,000.
Describing Snowden as "a fugitive who is currently in Russia", it urges Venezuela to keep him in custody if arrested and to seize all items in his possession for later delivery to the US. It provides a photograph and two alternative passport numbers – one revoked, and one reported lost or stolen.
Maduro said he did not accept the grounds for the charges.
"He has told the truth, in the spirit of rebellion, about the US spying on the whole world," Maduro said in his latest speech. "Who is the guilty one? A young man … who denounces war plans, or the US government which launches bombs and arms the terrorist Syrian opposition against the people and legitimate president, Bashar al-Assad?"
The Bolivian government, which has said it would listen sympathetically to an aslyum request from Snowden, said it too had turned down a pre-emptive US extradition request.
Ortega said Nicaragua had received an asylum request from Snowden and the president gave a guarded acceptance.
"We are an open country, respectful of the right of asylum, and it's clear that if circumstances permit, we would gladly receive Snowden and give him asylum in Nicaragua," Ortega told a gathering in Managua.
So far, the countries that have been most vocal in offering support are close allies of Venezuela. Ecuador has also expressed support for Snowden, though the government there has yet to decide whether it would grant aslyum. It is already providing refuge for the WikiLeaks founder Julian Assange, who has been in the Ecuadorean embassy in London for about a year.
Many in Latin America were furious when the Bolivian president's flight from Russia was denied airspace by European countries, forcing it to land in Vienna, where Morales had to spend more than half a day waiting to get clearance to continue his journey.
Morales said the Spanish ambassador to Austria arrived at the airport with two embassy personnel and asked to search the plane. He said he refused.
The Spanish foreign minister, José Manuel García-Margallo, acknowledged on Friday that the decision to block Morales plane was based on a tip that Snowden was on board.
"They told us that the information was clear, that he was inside," he told Spanish TV, without clarifying who the tip was from.
It is assumed the US was behind the diversion, though US officials have said only that they were in contact with the countries on the plane's route.
France has apologised to Bolivia.
Morales said when he finally arrived in La Paz: "It is an open provocation to the continent, not only to the president; they use the agent of North American imperialism to scare us and intimidate us."
At a hastily called meeting of the Unasur regional bloc, many governments condemned the action against Morales plane.
"We are not colonies any more," Uruguay's president, José Mujica, said. "We deserve respect, and when one of our governments is insulted we feel the insult throughout Latin America."
The Argentinean president, Cristina Fernandez de Kirchner, was also present, along with a senior representative of President Dilma Rousseff of Brazil.
Regional support may make it easier for the country offering asylum to resist US pressure for extradition. But whether Snowden can make it to South America remains uncertain, as are his current circumstances. He has not been seen or heard in public since he flew to Russia from Hong Kong. WikiLeaks says it is in touch with him and that he has widened his search for aslyum by adding six new countries.
In a tweet, the group said it would not reveal the names of the nations "due to attempted US interference".