British officials want to enforce an extradition warrant against Assange, who was given refuge in the Ecuadorian embassy in London June 19, the International Herald Tribune reported.
Assange is wanted in Sweden on sexual assault charges and in the United States for publishing thousands of top-secret documents.
"We are not a British colony," Ecuadorian Foreign Minister Ricardo Patino said in response to the threat.
Some Latin American countries are still agitated by what they view as British neo-colonialism when British forces invaded the Falkland Islands in 1982 after Argentine forces landed on the islands in a territorial dispute.
The threatened raid on the embassy was a likely topic for members of the Union of South American Nations, which was scheduled to meet Sunday in the Ecuadorian city of Guayaquil.
The Alianza Bolivariana, a socialist organization active in Ecuador, Venezuela, Cuba, Nicaragua and Bolivia, issued a statement rejecting the threat ahead of a meeting of the group's officials Saturday.