Oswaldo Payá, a dissident leader, delivered a petition to parliament in Havana demanding a referendum on human and democratic rights.
The petition, the second of its kind to be presented in the past two years, carried the signatures, names and addresses of more than 14,000 Cubans.
Mr Payá, a devout Christian backed by Cuba's Catholic church, says that under the terms of the country's constitution a referendum is compulsory.
When he presented the first petition 17 months ago, Mr Castro's regime responded by organising its own petition calling for a constitutional amendment, later approved by lawmakers, ratifying Cuba's socialist system as "untouchable".
Some 40 organisers of Mr Payá's petition, known as the Varela Project, were arrested in March and given prison sentences of up to 28 years as part of a group of 75 people accused of "serving a foreign power", in this case the US.
Mr Payá's petition refers to a clause in the constitution that allows for a referendum to be held if more than 10,000 people back it.