The lower house already backed a similar bill.
Kazakhstan's opposition has condemned the "people's initiative" by a self-styled citizens' forum as a ploy to avoid a presidential election scheduled for 2012.
The United States has criticized it as a setback for democracy.
The legislation asks Nazarbaev to amend the constitution and call a referendum.
Supporters say they have collected more than 2.5 million signatures of citizens in favor of a referendum.
The 70-year-old Nazarbaev, who has ruled Kazakhstan for more than 20 years, has to give his final word on the referendum.
Scattered protests by opponents of the referendum have been met with arrests and the dispersal of demonstrations in various cities.
Outgoing U.S. Ambassador to Kazakhstan Richard Hoagland used his final news conference in Astana to criticize the referendum, saying Kazakhs "should have a bigger choice than simply 'yes' or 'no'" in order "to have a democratic voice in their country."
compiled from agency and RFE/RL reports