"Sometimes a handshake is just a handshake, but when the leader of the free world shakes the bloody hand of a ruthless dictator like Raul Castro, it becomes a propaganda coup for the tyrant," she said.
"Just as Mandela was released after 27 years in prison, Castro should finally release his political prisoners; he should hold free elections, and once and for all set the Cuban people free," Ted Cruz's spokesman Sean Rushton said Tuesday.
Still others were hopeful over the handshake and hoped that it would thaw the relations between the two countries that have only had one other exchange in the last 60 years.
"It's extraordinarily symbolic, and this opportunity must not be missed. Now the next step is to start talking," Cuban political scientist Esteban Morales said.
"What happened is a sign that the two countries are ready to negotiate."