Announcing the historic move aimed at normalisation of ties between the Cold War foes, President Obama said many Americans and Cubans were making a "choice between the future and the past".
He also urged critics in Congress to endorse his move by lifting the decades-old US trade embargo against Cuba.
"Americans and Cubans alike are ready to move forward. I believe it's time for Congress to do the same," he said, adding that, "We've already seen members from both parties begin that work."
But the Congress - House of Representatives and Senate, controlled by Republicans, has shown little sign that it intends to end the embargo. Several Republican candidates eying the White House in 2016 expressed their opposition to the historic shift in policy.
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Texas Senator Ted Cruz was quick to criticise Obama's move to reopen embassies in Havana and Washington from July 20, a major step towards normalisation of ties between the Cold War foes.
In a statement, Florida Senator Marco Rubio vowed to oppose the confirmation of an ambassador to Cuba until the Castro regime makes several concessions, including "securing greater political freedoms for the Cuban people."
Former Texas Governor Rick Perry said the Cuban government had made no changes that suggest re-engagement would benefit Cuban citizens.
"The Cuban people today are not any freer politically or economically, and President Obama has failed to account for what the Castro regime has done in the last several years that warrants such an enormous shift in a longstanding US policy," he said.