Currently, stranded at the Moscow airport for more than a week now, CIA whistleblower Snowden had sought asylum in more than two dozen countries, including India.
The US had warned countries not to give asylum to Snowden arguing that he is wanted on charges of espionage and leaking classified information.
India and majority of the countries where Snowden had sought asylum had refused his application.
But simultaneous announcements by presidents of Nicaragua and Venezuela offering asylum could be seen as a big disappointment for the US, which had been asking countries not to grant Snowden an asylum and he be returned to the country.
"The government of the Bolivarian Republic of Venezuela (has) decided to offer humanitarian asylum to the young American Edward Snowden so that he can live (without) persecution from the empire," President Nicolas Maduro told a military parade marking Venezuela's independence day.
Nicaragua President Daniel Ortega also made a similar offer, but did not elaborate further. "It's clear that if the circumstances permit it we will gladly receive Snowden and will grant him asylum here in Nicaragua," he said.
"We have the sovereign right to help a person who felt remorse after finding out how the United States was using technology to spy on the whole world, and especially its European allies," Ortega said.
Refusing to comment on the asylum offers by Nicaragua and Venezuela, the White House referred it to the Department of Justice, which handles all issues related to asylum.
"He (Snowden) has been accused of leaking classified information, he's been charged with three felony counts and should be returned to the United States," State Department spokesperson Jen Psaki had told reporters early this week.
Such defiance by Venezuela and Nicaragua, The New York Times reported, appeared to be linked to outrage in Latin America over the treatment last week of Bolivian President Evo Morales, whose plane was denied permission to fly over several European countries because of what Bolivian officials said were unfounded suspicions that Snowden was aboard.
Morales was on his way home from a meeting in Moscow.
Earlier, Wikileaks said on Twitter, the micro blogging site, that 30-year-old former National Security Agency contractor Snowden has sought asylum from six more countries.
It said all these asylum requests have been submitted at the embassies of these countries in Moscow. It refused to reveal the name of six new countries where Snowden had applied to for asylum, due to "attempted US interference".
Snowden reached Moscow from Hong Kong where he had fled from the US after leaking the secretive American surveillance programme, which has caused outrage in many parts of the world including key American allies and partners in Europe.
Since his passport has been cancelled, Snowden can't buy a plane ticket to fly to his destination. As a result of which he has been desperately seeking asylum requests.