Rubio's remarks came as Washington seeks to pressure Havana into political reforms.
Cuban Foreign Minister Bruno Rodriguez, in the same address, reaffirmed Havana's willingness to engage in dialogue, a stance that contrasts with the US's hardline rhetoric.
The United States has maintained a trade embargo against Cuba since 1960, tightening it during the Trump administration with new sanctions on Cuban state enterprises and restrictions on travel.
Rubio also linked Cuba's plight to Venezuela, urging free and fair elections there, and criticized the Maduro regime's lack of accountability.
The next step will be a review of the embargo policy by the Biden administration, which may adjust sanctions in response to the new diplomatic overtures.
Meanwhile, Cuban citizens face fuel shortages and power blackouts, underscoring the urgency of the reforms Rubio calls for.