Democratic lawmakers have said allowing gay couples to marry is one of their top priorities.
A similar bill died two years ago. But Senate President Stephen Sweeney, who abstained then, now favors allowing same-sex unions.
Two gay rights groups also have filed a lawsuit to try to force the state to recognize gay marriage.
New Jersey now offers civil unions, which offer the legal protections of marriage. But gay rights groups say civil unions are confusing and create a separate and inherently unequal status for gay couples.
Some social conservatives say allowing gay marriage would weaken the institution for heterosexual couples.
