Also on Friday, Daniel Ortega, the president of Nicaragua, said he was open to taking in Mr. Snowden. “It is clear that if the circumstances permit we will take in Mr. Snowden with pleasure and give him asylum in Nicaragua,” Mr. Ortega said in Managua.

Mr. Snowden has sought asylum from more than two dozen nations. Most countries have declined.

The offers from Venezuela and Nicaragua appeared to be linked to outrage in Latin America over the treatment last week of President Evo Morales of Bolivia, whose plane was denied permission to fly over several European countries because of what Bolivian officials said were unfounded suspicions that Mr. Snowden was aboard. Mr. Morales was on his way home from a meeting in Moscow.

Mr. Maduro had previously voiced sympathy for Mr. Snowden. He frequently bashes the United States, depicting it as an imperialist bully in Latin America. But at the same time he has shown a desire to improve relations with the United States, directing his foreign minister to start talks with Washington aimed at smoothing the rocky relationship with the top buyer of his country’s all-important oil exports.

Earlier on Friday, WikiLeaks said in a post on Twitter that Mr. Snowden, who is wanted by the United States on charges of revealing classified government information, “has applied to another six countries for asylum,” following up on similar applications to about 20 nations last week.

Supporters of Mr. Snowden clearly blame the refusals on pressure from the United States, and, as a result, WikiLeaks said it would not reveal the latest countries in which he is seeking shelter. “They will not be named at this time due to attempted US interference,” the group wrote on Twitter.