In his first public announcement since fleeing Hong Kong eight days ago, he accused Obama of ordering his Vice President Joe Biden to put pressure on leaders of countries where he was seeking asylum.
"On Thursday, President Obama declared before the world that he would not permit any diplomatic 'wheeling and dealing' over my case," Snowden said in statement issued to the WikiLeaks site.
"Yet now it is being reported that after promising not to do so, the President ordered his Vice President to pressure the leaders of nations from which I have requested protection to deny my asylum petitions," he added.
It also emerged that Snowden had written to Ecuador's President Rafael Correa thanking him for his support in his bid to avoid extradition.
"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 wrote in the letter, obtained by Britain's Press Association.
Correa has said Biden raised the issue of Snowden in a conversation over the weekend, asking him to reject the fugitive computer analyst's asylum request.
Snowden, in his statement issued from his refuge at Moscow's Sheremetyevo airport, said Obama was guilty of "deception" and imposing "the extralegal penalty of exile.
"These are the old, bad tools of political aggression," he continued.
"Their purpose is to frighten, not me, but those who would come after me."
The Obama administration had rejected the US Universal Declaration of Human Rights and had chosen "the strategy of using citizenship as a weapon," he said.
"Although I am convicted of nothing, it has unilaterally revoked my passport, leaving me a stateless person," he added.
"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."
Snowden, whose passport has been revoked by the US, singled out Fidel Narvaez, the Ecuadorian consul in London, for praise in helping him evade capture.
WikiLeaks founder Julian Assange revealed last week that Narvaez had issued Snowden with a refugee travel document, which had allowed him to flee Hong Kong eight days ago as Washington pressed for his extradition.
Correa said on Saturday that the London consul had overstepped his authority in issuing the paper.
As well as seeking asylum in Ecuador, Snowden has also applied for asylum in Russia.
Russian President Vladimir Putin said Monday Snowden was welcome to stay as long as he stopped leaking US intelligence reports.
But in his statement posted to WikiLeaks, Snowden concluded: "I am unbowed in my convictions and impressed at the efforts taken by so many."