Colombian President Juan Manuel Santos said it would be "unacceptable" to exclude Cuba in the future, and Bolivian President Evo Morales echoed that sentiment.
An alliance of left-leaning Latin American countries called ALBA -- Venezuela, Ecuador, Bolivia, Nicaragua, Cuba, and several smaller countries -- issued a statement saying members will not participate in future Summits of the Americas unless Cuba is invited.
Washington argues that Cuba lacks the necessary democratic credentials to be included.
Cuba was expelled from the U.S.-backed Organization of American States in 1962, a move that was rescinded in 2009. But Cuba has declined to return to that group.