JEFFERSON CITY, Mo. — A bill to give some of the nation’s broadest legal protections to opponents of same-sex marriage took a crucial step forward in Missouri on Wednesday, winning approval in the State Senate after Republicans used a rare procedural move to break a 39-hour filibuster by Democrats.

Since the Supreme Court’s ruling in June legalizing gay marriage, legislators in many states have introduced bills that they say would protect religious freedom and that opponents say would permit discrimination. In some respects, the Missouri bill would go beyond any law now in place, prompting challenges that could keep the issue before the courts for years.

The bill, a proposed amendment to the state Constitution, would shield religious groups and businesses from having to facilitate same-sex weddings. Opponents contended that the bill was probably unconstitutional, and that the wording could lead to much broader consequences, like denying social services, education, employment or housing to married gay people.

Democrats began a filibuster on Monday, but with Republicans holding an overwhelming Senate majority, it was clear that opponents could only delay the bill. The General Assembly allows lawmakers to cut off a debate by submitting a letter signed by a simple majority of the members; the rule is often invoked in the House, but rarely in the Senate.