MEXICO CITY — Cuban lawmakers on Sunday approved a draft of a new Constitution that would seek to modernize the nation by recognizing the right to own private property and opening the door to the possible legalization of same-sex marriage, among other economic, political and social changes.

The document would also encourage foreign investment and strengthen the judicial system, including recognizing the presumption of innocence.

The draft Constitution would significantly reorganize the government. It calls for creating the position of a prime minister, who would share power with the president, and governorships for the nation’s provinces.

Before it can become official, the document, which would replace the current 1976 Soviet-era Constitution, will be put before the public in a series of meetings around the country and then be voted on in a national referendum, a process expected to take months.