Edward Snowden has accused the US of persecution and claims he is free to publish information "that serves the public interest" in a letter to Ecuador authorities.
The former NSA contractor has broken his silence for the first time since he fled to Moscow eight days ago and thanked the South American country for helping him get to Russia.
It comes after a British WikiLeaks activist who is travelling with Snowden handed an asylum application to a Russian consulate in the transit area of Moscow's Sheremetyevo airport on Sunday night, according to a Russian foreign ministry official.
"At 10.30pm (1830 GMT) yesterday, British citizen Sarah Harrison turned up at the consulate department at Sheremetyevo airport and submitted a request from Snowden about granting him asylum," the AFP news agency quoted consulate officer Kim Shevchenko as saying.
Mr Snowden has been on the run since leaking information about the US government's secret surveillance programme Prism to The Guardian and The Washington Post in early June.
He initially fled from Hawaii to Hong Kong, but was allowed to leave the country after what Hong Kong officials claim was a clerical error on the part of the US government.
In his letter to Ecuadorian authorities, Mr Snowden wrote: "There are few world leaders who would risk standing for the human rights of an individual against the most powerful government on earth, and the bravery of Ecuador and its people is an example to the world."
He also attacked the US authorities who have annulled his passport and demanded his extradition.
"While the public has cried out support of my shining a light on this secret system of injustice, the government of the United States of America responded with an extrajudicial man-hunt costing me my family, my freedom to travel and my right to live peacefully without fear of illegal aggression," he wrote.
"As I face this persecution, there has been silence from governments afraid of the United States government and their threats. Ecuador however, rose to stand and defend the human right to seek asylum."
But Ecuador has been coy over offering him shelter.
After the asylum request in Russia became public, Ecuador's President Rafael Correa said the application "could definitely resolve Mr Snowden's situation".
Russia has rejected US calls to hand over Snowden, saying that because he remains in the airport transit zone he has not officially crossed the Russian border. Therefore, they claim, they are powerless to act.
But on Monday, Russian President Vladimir Putin and US President Barack Obama ordered the heads of their security agencies, the FBI and FSB, to find a solution to the impasse, according to the head of Russia's Security Council Nikolai Patrushev.
Speaking to the state television channel Rossiya 24, he said: "Of course (Putin and Obama) don't have a solution that would work for both sides, so they have ordered the FSB director (Alexander) Bortnikov and FBI director Robert Mueller to keep in constant contact and find solutions."
Mr Putin told a news conference that "we should let professionals decide", and said Russia "never hands over anybody anywhere".
He added: "Snowden is free to go but if he decides to stay, he has to stop his work directed to hurt our American partners. I know that this kind of statement sounds strange from me."
Mr Obama confirmed that there were high-level consultations between Moscow and Washington over Snowden's fate.
"We have gone through regular, law enforcement channels in enforcing the extradition request that we have made with respect to Mr Snowden," he said while on his African tour.
"Mr Snowden, we understand, has travelled there without a valid passport, without legal papers. We are hopeful that the Russian government makes decisions based on the normal procedures regarding international travel."
The US state department said the whistleblower could be given a "one entry travel document" to return home and as US citizen was guaranteed a "free and fair trial".
However, in another letter released by WikiLeaks, Mr Snowden accused the Obama administration of using "citizenship as a weapon".
"Although I am convicted of nothing, it has unilaterally revoked my passport, leaving me a stateless person. Without any judicial order, the administration now seeks to stop me exercising a basic right. A right that belongs to everybody. The right to seek asylum, " he wrote.
The apparent asylum request came as the EU confronted the US over allegations it bugged offices in Brussels and America.