Spanish Foreign Minister Jose Manuel Garcia-Margallo has said Cuba's economic opening "will translate into a political opening is inevitable."
"Another thing is the speed at which this will take place, and this is something that depends fundamentally on the regime," Margallo told daily newspaper ABC.
Garcia-Margallo also called for national reconciliation in Cuba and within Cuban diaspora as well as an amnesty for dissidents.
Cuba, a communist country, was embargoed by the European Union from 2003 until 2008.
Cuba opened its Washington mission after 54 years of frozen relations last July. President Barack Obama and his Cuban counterpart Raul Castro exchanged the letters agreed to restore ties on July 20. This was the signal of the new stage of diplomatic relations for both countries.
Other countries have also been looking for a way to link with Cuba in economically. French President Francois Hollande recently visited Havana to improve economic relations between France and Cuba.