Cuban law requires 10,000 signatures for a referendum
The petition - the first of its kind by Cuba's small dissident movement - comes ahead of an unprecedented visit to Havana by the former American president, Jimmy Carter.
The BBC correspondent in Cuba says that while the petition is likely to grab Mr Carter's attention, the communist government has made clear it has little chance of success.
Leading dissident Oswaldo Paya and two other local activists entered the Cuban National Assembly carrying two white cardboard boxes containing the lists of 11,020 signatures.
Election call
"A new moment has begun for our nation, a moment of reconciliation," Mr Paya said afterwards.
Project Varela, as the campaign is called - named after Cuban independence hero Felix Varela - seeks a vote on civil liberties including freedom of speech, an amnesty for political prisoners, support for private business, a new electoral law and a general election.
It is seen as the biggest domestic, non-violent campaign to force reforms in the government established by President Fidel Castro 43 years ago.
Cuba's constitution says the National Assembly should schedule a national referendum if it receives the verified signatures of 10,000 legal voters.
Mr Paya said that of the 20,000 signatures activists gathered in recent months, volunteers had verified 11,020.
Foreign interference
"The heroes are these Cubans, more than 20,000 who signed this demand for an opening in a written declaration," Mr Paya said as he handed the petition over.
"All of these Cubans, who with great courage and sacrifice have signed Project Varela, are the social vanguard for peaceful change in Cuba," Mr Paya added.
There was no immediate response from Castro's government to the move who in the past have dismissed the project as a plot financed by the United States that will fail.
Mr Paya says the project has received no money from any government or group outside Cuba.
Carter mission
He also accused Cuban state security agents of harassing the group as they gathered the signatures.
The petition comes just 48-hours before the arrival of Mr Carter who is planning a six-day visit to improve relations between the US and Cuba and discuss human rights issues.
Mr Carter, a critic of the US trade embargo against Cuba, is scheduled to meet Mr Castro three times in the course of the trip.
In an apparent gesture toward Mr Carter, Cuban authorities released the island's most famous dissident, Vladimiro Roca, on Sunday - two months before he completed a five-year jail sentence on charges of subversion.