BATON ROUGE (AP) — A plan to return the state to an open primary system for congressional elections is one step from passing the legislature, after the state Senate approved it Tuesday despite opposition from Republican and Democratic party leaders.

An open primary would allow all candidates, regardless of party, to run against each other on the same primary ballot.

Before passing the bill 31-5, the Senate changed it to take effect with the fall elections, instead of 2012 as the House had OK’d. The proposal by Rep. Hunter Greene, R-Baton Rouge, returns to the House for approval of the date change before it can head to the governor.

A spokesman for Gov. Bobby Jindal has said he wouldn’t veto the measure if lawmakers send it to his desk, but it was unclear if the change in the effective date would create problems for the proposal in the House.

Greene said he would discuss the matter privately with House members before deciding whether he would support the change.

The bill would do away with Democratic and Republican primaries and run congressional elections in the same manner as those on the state and local levels.

All candidates for Congress would run against each other in a November election, with the top two vote-getters advancing to a December runoff if no candidate wins more than 50 percent of the vote.

Currently, voters cast ballots in Republican and Democratic primaries, an October party primary runoff if needed and then a November general election, to select their congressmen and U.S. senators. The change began with the 2008 elections after decades under an open primary system.

Supporters of switching back argue it would save the state $6.6 million every two years and would end a confusing system that runs different primaries for state and federal elections.

‘‘We shut out people who wanted to vote, and we created absolute confusion,’’ said Sen. Robert Adley, R-Benton.

The open primary bill has moved with surprising ease in the legislative session. Even supportive lawmakers have acknowledged they didn’t expect it to get such quick and overwhelming backing.

The leaders of both the state Democratic and Republican parties have opposed the move, arguing it would diminish the seniority of Louisiana’s members of Congress because some could be elected in December, a month later than in most other states. Louisiana Democratic Party Chairman Buddy Leach also said open primaries too often allow ‘‘candidates on the political extremes’’ to make it to the general election.

Voting against the bill were Sens. Sharon Broome, D-Baton Rouge; Elbert Guillory, D-Opelousas; Karen Carter Peterson, D-New Orleans; Neil Riser, R-Columbia; and Mike Walsworth, R-West Monroe.