Castro called Snowden a man persecuted for his ideals but did not say whether Cuba would offer him refuge or safe passage. That is a key issue, as his simplest route to Latin America could be one of five direct flights that Russian carrier Aeroflot operates to Havana each week.
From there, Snowden could fly to Venezuela, Bolivia or Nicaragua—all possible destinations for him.
Despite Castro's speech, it is not clear whether the communist-run country wants to risk torpedoing mildly improved relations with the United States by letting Snowden transit through the island.
He was booked on an Aeroflot flight to Havana two weeks ago but did not board the plane. The flights normally pass through U.S. airspace, raising the possibility they could be intercepted.
"We support the sovereign right of .... Venezuela and all states in the region to grant asylum to those persecuted for their ideals or their struggles for democratic rights," Castro said in the address to Cuba's national assembly.
The 82-year-old Cuban leader said his country was aware of the kind of secretive NSA programs Snowden revealed. As a longtime enemy of Washington, the Caribbean nation has been "one of the most harassed and spied-upon nations on the planet," he added.
He also brought up the case of Luis Posada Carriles, an anti-Castro militant wanted in both Venezuela and Cuba for the 1976 bombing of a Cuban passenger plane that killed 73.
Posada Carriles has been living in the United States since 2005. Multiple legal efforts to deport him have failed.
Snowden has been out of sight in the transit area of Moscow's main airport since he suddenly appeared there on a plane from Hong Kong two weeks ago.
Over the weekend, Venezuela and Bolivia made asylum offers to Snowden, and Nicaragua has said it is considering his request.
The case continued to have ramifications across Latin America. Brazil said Sunday that it was worried by a report that the United States has collected data on billions of telephone and email conversations in the country.
The O Globo newspaper reported that information released by Snowden shows that the number of telephone and email messages logged by the NSA in Brazil in January alone was not far behind the 2.3 billion reportedly collected in the United States.
Foreign Minister Antonio Patriota expressed "deep concern at the report that electronic and telephone communications of Brazilian citizens are being the object of espionage by organs of American intelligence.
"The Brazilian government has asked for clarifications" through the U.S. Embassy in Brazil and Brazil's embassy in Washington, he said.
Patriota also said Brazil will ask the U.N. for measures "to impede abuses and protect the privacy" of Internet users, laying down rules for governments "to guarantee cybernetic security that protects the rights of citizens and preserves the sovereignty of all countries."