Kennedy said that the Fidel Castro revolution "betrayed the ideals of the Cuban revolution and the hopes of the Cuban people".
According to the Ecuadorian leader, today the peoples of Latin America are united as never before.
"I think the question for the president is, in terms of making policy, are we going to be rooted in that past, or are we going to look to the future?"
Cuba used to be the colony of the Spanish Empire for centuries, until 1898, when as a result of the Spanish-American War, it came under the U.S. control.
Castro, who ruled from 1959 until an illness forced him to hand power to his brother Raul in 2006, died Friday at age 90.
White House Press Secretary Josh Earnest on Tuesday said President Barack Obama will not send an official presidential delegation to Cuba for Fidel Castro's memorial service, instead opting to send two top diplomats to represent the United States.
President Nicolas Maduro of Venezuela, Evo Morales of Bolivia and Daniel Ortega of Nicaragua were among the foreign dignitaries who paid their respects to Castro. The Kremlin said he held a different view on his legacy to that of Trump, who has called the Cuban leader "a brutal dictator".
Supporters say he returned Cuba to the people and praise him for some of his social programmes, such as public health and education.
Ben Rhodes, the deputy national security adviser, and Jeffrey DeLaurentis, the top US diplomat to Cuba, will attend the service, ABC News reported.
An earlier version of this story incorrectly stated that Rhodes and DeLaurentis would attend Castro's funeral.
Sending an official delegation could also risk exacerbating differences between Obama and his successor Donald Trump, who has threatened to "terminate" the US-Cuba thaw.
The event was part of week-long commemorations honouring Castro. Many state employees and school children came together in groups.
A caravan carrying Castro's ashes will depart Havana on Wednesday en route to the eastern city of Santiago de Cuba, his final resting place, in a reversal of the journey he took with the rebel army that overthrew Fulgencio Batista in 1959.