The code was approved by parliamentarians in the National Assembly and will be put to the public in a vote, which Diaz Canel said was unprecedented.
The new code would legalise same-sex marriage and civil unions, allow same-sex couples to adopt children and promote equal sharing of domestic responsibilities.
Canel said it does not aim to build a certain type of family, but promotes respect for the rights of all people, as reflected in the Constitution.
While its adoption has met resistance from the Catholic Church, polls suggest a majority of Cubans support the legislation.
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