The tensions flared to new heights after Venezuela's leader, Nicolas Maduro, a fast friend and ally of Cuba, was captured by US forces last month and brought to the US.
Cuba, which received discounted or free Venezuelan oil, is facing an economic crisis with the energy cutoff.
The US has wielded the oil weapon with expectations that a worsening crisis would topple the Cuban government headed by President Miguel Díaz-Canel.
"Cuba needs to change, it needs to change dramatically because it is the only chance that it has to improve the quality of life for its people," said Rubio, the son of Cuban exiles.
The mystery boat brought back memories of the Bay of Pigs incident in 1961, when a band of Cuban exiles with Washington's clandestine help launched a failed attack by sea on Fidel Castro's government.
Frequently, boats are used to smuggle people out of Cuba and shootings involving them and Cuban forces have been reported.
Earlier this month, Trump issued an order allowing US forces to intercept US boats heading to Cuba because of the extreme danger they would face.
(With inputs from IANS)
