In an interview given to Reuters and others ahead of the first anniversary of his seeking refuge in the Ecuadorean embassy in London, Assange said he was concerned by reports that Britain had told airlines to stop Snowden from flying to London.
A spokesman for Britain's Home Office declined to comment on reports Britain had told airlines around the world to block Snowden, as did a spokesman for Prime Minister David Cameron.
"The British government refused entry to this country of Edward Snowden. Why? Presumably because it doesn't want to end up with another Julian Assange," Assange said.
"The British government should be offering Mr Snowden asylum, not excluding him. I'm sure if you ask the population of the UK what they want, they want to protect Mr Snowden."
Assange, who remain in Ecuador's embassy for fear of arrest over Swedish sex allegations and possible extradition to the United States over Wikileaks' disclosure of U.S. government documents, said Britain's decision to block Snowden was misguided.
"The rule of law has come under strain in the UK. This is another example. The United Kingdom doesn't want to say no to the United States under any circumstances. Not in my case, and not in the case of Mr Snowden."
When asked about his own contacts with Snowden, Assange said he couldn't comment on "source-related issues".
Ecuadorean Foreign Minister Ricardo Patino is due to meet British Foreign Secretary William Hague in London on Monday to discuss Assange's case.
Assange denies the sexual allegations against him by two women in Sweden, but his supporters say they fear Sweden would extradite him to the United States if he agreed to go there.
Assange said he was encouraged by Snowden's actions.
"In the United States the ideals that I have fought for for so long are now catching on, being embodied in the extraordinary courage of individuals such as Edward Snowden. The renewed political and popular support for whistleblowers such as Edward Snowden shows that the times are changing."
© Thomson Reuters 2013