Venezuela's Nicolas Maduro said it would give asylum to the intelligence leaker, who is believed to be holed up in a transit area of Moscow airport.
Meanwhile Nicaraguan President Daniel Ortega said his country would do so "if circumstances permit".
Wikileaks said Snowden had applied to six additional countries on Friday.
The whistleblowing website said it would not name the countries "due to attempted US interference".
Snowden has already asked 21 countries for asylum, most of whom have turned down his request mostly due to US pressures on governments that might consider cooperating with him.
President Maduro made his announcement in a speech on Venezuela's Independence Day.
"As head of state and government of the Bolivarian Republic of Venezuela I have decided to offer humanitarian asylum to the young US citizen Edward Snowden so he can come to the fatherland of Bolivar and Chavez to live away from the imperial North American persecution," President Maduro said.
Earlier in June, he leaked confidential information that showed the NSA collects data of phone records and Internet communication of American citizens.
Washington, which says Snowden must be tried on espionage charges for disclosing government spying programs, had ordered some European countries to prevent the flight carrying Bolivian President Evo Morales from using their airspace on Tuesday over alleged suspicion that the whistleblower was on board the plane.
The United States has revoked Snowden’s passport, depriving him of the necessary documentation with which to travel.
According to some other documents provided by Snowden, the US has been also spying on EU offices in Washington, DC, New York, and Brussels.
On Thursday, a resolution adopted in the European Parliament, strongly condemned the US “spying on EU representations” and called for “immediate clarification from the US authorities on the matter.