Mr. Correa, speaking on his weekly television broadcast, said that the two had a "cordial" conversation on Friday initiated by Mr. Biden, but said he could not decide on Mr. Snowden's request until he entered Ecuador.
The fallout from Mr. Snowden's disclosures widened Saturday, as the German magazine Der Spiegel reported that the United States had eavesdropped on European Union offices in Washington, Brussels and at the United Nations in New York. Mr. Snowden, a former National Security Agency contractor who revealed details about American surveillance programs, fled to Hong Kong last month and then left there last week in a bid to find a haven to escape charges of violating espionage laws in the United States. He arrived in Moscow last Sunday, where he has remained out of sight, apparently cloistered in a transit area of the airport there.
Ecuadorean officials have said that Mr. Snowden asked them for asylum. But after initially signaling that his government was studying the request, Mr. Correa said Thursday that under his country's laws, the request could not be processed unless Mr. Snowden was in Ecuador or one of its embassies.
In Washington, Bernadette Meehan, a National Security Council spokeswoman, called the discussion between Mr. Correa and Mr. Biden "a broad conversation regarding the bilateral relationship."
"They did discuss Mr. Snowden, but we are not going to provide details on their discussion," she said in an e-mail.
Still, Mr. Biden's call to Mr. Correa, the highest-level contact between an American official and the Ecuadorean president since revelations about Mr. Snowden's role in releasing classified N.S.A. documents, raised new questions about whether Ecuador is having qualms about granting asylum to Mr. Snowden.
White House officials have said in recent days that in their contacts with foreign governments about Mr. Snowden, they have warned those governments about the felony charges that Mr. Snowden faced in the United States and urged that they not further aid his international flight.
Mr. Correa regularly denounces the United States, calling it an imperialist power that tries to bully small countries like Ecuador. But he said he told Mr. Biden that Ecuador would take the opinion of the United States into account if it eventually had to make a decision in the case.
He contrasted Mr. Biden's courteous attitude with what he has characterized as the bad manners of some members of Congress who have threatened to end trade benefits for Ecuador's exports to the United States if the country decides to give refuge to Mr. Snowden.
The Ecuadorean president also said last week that Ecuadorean officials had had little contact with Mr. Snowden since his arrival in Moscow.
Mr. Correa said Thursday in a news conference: "The only contact that there has been given Mr. Snowden's asylum request, which the foreign minister made public, is that the ambassador went to see him in the Moscow airport. He wasn't able to see him the first day, according to what the ambassador informed me, but he saw him the second day. He saw that he was in good health. He repeated his desire that Ecuador grant him asylum. Since then we really haven't had any further contact."
It is not clear how Mr. Snowden could get to Ecuador or one of its embassies. The United States has revoked his passport, and Mr. Correa denied reports that Ecuador gave him papers permitting him to travel internationally.
Last year, Ecuador granted asylum to Julian Assange, the founder of WikiLeaks, who has been stuck in the country's embassy in London ever since.
On Saturday, Der Speigel reported that it was able to review "top secret" N.S.A. documents in Mr. Snowden's possession dated September 2010 that showed that the agency had infiltrated European Union computers in two locations to monitor telephone conversations, e-mails and other documents.
The magazine said that surveillance devices were installed in the European Union's offices in Washington and that the organization's computer networks in Brussels had been infiltrated.
The lead writer of the article was Laura Poitras, 49, a documentary filmmaker who emerged as the pivotal connection between Mr. Snowden and writers for The Guardian and The Washington Post who published his leaked documents about government surveillance. She has shared bylines with reporters of those publications in their coverage of the N.S.A. leaks.
If Mr. Snowden, through Ms. Poitras, showed parts of his trove to Der Spiegel, it would mark an expansion of his journalistic collaborations, which so far have included The Guardian, The Post and The South China Morning Post of Hong Kong. The Morning Post reported this month that Mr. Snowden had provided detailed data showing the dates and Internet protocol addresses of specific computers in mainland China and Hong Kong that the N.S.A. penetrated over the last four years.
Maggy Ayala contributed reporting from Quito, and Eric Schmitt from Washington.