By Lawrence Hurley

WASHINGTON (Reuters) - Big business rallied behind the gay marriage cause on Thursday as the U.S. Supreme Court scheduled oral arguments for April 28 on the contentious social issue that promises to yield one of the justices' most important rulings of 2015.

A total of 379 businesses and groups representing employers across various sectors, including Google Inc, American Airlines Group Inc, Goldman Sachs Group Inc and Johnson & Johnson, have signed on to a friend-of-the-court brief in support of gay marriage that was filed on Thursday.

Various supporters of gay marriage are filing similar briefs ahead of a Friday deadline. One was filed on behalf of dozens of prominent conservatives, including former Republican National Committee Chairman Ken Mehlman and David Koch, one of the billionaire Koch brothers known for donating to right-leaning political causes.

The brief says that "conservative values are consistent with - indeed, are advanced by - affording civil marriage rights to same-sex couples."

The administration of President Barack Obama is also due to file a brief backing gay marriage.

The court must decide whether states have the right to ban gay marriage. The nine justices will hear an extended 2-1/2-hour argument in cases concerning same-sex marriage bans in Ohio, Michigan, Kentucky and Tennessee.

The justices will consider whether same-sex marriage bans are prohibited by the U.S. Constitution's guarantee of equal protection under the law. A ruling is due by the end of June.

There are currently 37 states where gay marriage has been allowed to proceed, although a legal battle is ongoing in Alabama, with the state's top court putting it on hold.

The Supreme Court cases come two years after the high court set off a wave of pro-gay marriage rulings by invalidating a federal law that restricted benefits to heterosexual couples.

At the time of that June 2013 ruling, only 12 of the 50 states permitted gay marriage.

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Businesses also backed gay marriage advocates in the previous Supreme Court case.

In the new brief, lawyers with the Morgan Lewis law firm said that inconsistent state laws impose burdens on business and that marriage bans can conflict with corporate anti-discrimination and diversity policies.

"Allowing same-sex couples to marry improves employee morale and productivity, reduces uncertainty, and removes the wasteful administrative burdens imposed by the current disparity of state law treatment," the brief says.

Thomson Reuters Corp, which owns Reuters news, also signed on to the brief.

(Reporting by Lawrence Hurley; Editing by Will Dunham and Eric Beech)