Speaking to reporters in Hanoi, Foreign Minister Ricardo Patino said he could not comment on Snowden's location after the U.S. fugitive did not board a flight from Moscow to Cuba on which he was booked.
"I cannot give information with respect to that ... we cannot offer specific information about the specific situation of Mr. Snowden at this moment," he said.
Patino did not say how long it would take Ecuador to decide on Snowden's asylum request, which he said "has to do with freedom of expression and with the security of citizens around the world."
Snowden had been in hiding in Hong Kong for several weeks after revealing the spy programs. He flew to Moscow on Sunday and was booked on an Aeroflot flight to Cuba on Monday, but an airline representative said he didn't board the plane and AP reporters on the flight couldn't see him.
Patino said Ecuador was in touch with the highest authorities of Russia about the case.
"The government of Ecuador has maintained a respectful diplomatic contact with the government of Russia and has informed it that Ecuador is considering the petition for asylum on the part of Mr. Snowden," he said.
Patino read a letter from Snowden to Ecuador's president in which he asked for asylum "due to the risk of persecution by the government of the United States and its agents."
Snowden said in the letter that he revealed the information about the highly classified spy programs because the U.S. "is intercepting the majority of communications of the world."
"I have been accused of being a traitor" and "there have been calls for me to be executed or imprisoned," the letter said. He said it was unlikely that he could receive a fair trial.
Patino said Ecuador would not base its asylum decision on its potential to damage the country's relationship with the United States.
" There are some governments that act more upon their own interests, but we do not," Patino said. "We act upon our principles."
He added, "We take care of the human rights of the people."
Anti-secrecy group WikiLeaks earlier said Snowden was bound for Ecuador "via a safe route for the purposes of asylum, and is being escorted by diplomats and legal advisers from WikiLeaks." The organization's founder, Julian Assange, was granted asylum by Ecuador last year and has been staying at the country's embassy in the United Kingdom to avoid extradition to Sweden to face questioning about sex crime allegations.
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