(Reuters) - President Joe Biden followed through on Friday on his vow to veto a Republican-backed measure that would have repealed a U.S. labor board rule treating companies as the employers of many of their contract and franchise workers and requiring them to bargain with those workers' unions.

The proposal to repeal the National Labor Relations Board rule passed Congress narrowly and it is unlikely Republicans can muster the two-thirds majority to override the veto by Biden, a Democrat. A federal judge in March blocked the rule from taking effect, but that decision will likely be appealed.

In a memo to lawmakers, Biden said the board's rule would ensure that employers cannot evade their legal obligations by controlling workers indirectly through contractors.

"Republicans are siding with union-busting corporations over the needs of workers and their unions," Biden said.

An NLRB spokeswoman declined to comment. Some Republican backers of the resolution did not immediately respond to requests for comment.

The rule would treat companies as "joint employers" of contract and franchise workers when they have control over key working conditions such as pay, scheduling, discipline and supervision, even if that control is indirect or not exercised.

Critics of the rule, including many Republicans and most major business groups, have said it would be improper to force companies to the bargaining table when they have little control over working conditions.

Groups representing franchise businesses say it could upend the franchise model by requiring companies such as McDonald's to bargain with the employees of franchisees.

Matthew Haller, president and CEO of the International Franchise Association, said the rule would cause particular harm to underrepresented groups including minorities, women and veterans who have often turned to franchising as a path to business ownership.

"President Biden claims to be a champion for small businesses, but today he turned his back on franchising," Haller said in a statement.

The rule was set to take effect in February, but was delayed and ultimately blocked by U.S. District Judge J. Campbell Barker in Tyler, Texas, in a lawsuit by the U.S. Chamber of Commerce and other business groups.

Barker, an appointee of Republican former President Donald Trump, said the rule was invalid because it would treat some companies as employers even when they lacked any meaningful control over the working conditions of contract and franchise workers.

The board has until later this month to appeal Barker's ruling.

(Reporting by Daniel Wiessner in Albany, New York; Editing by Emelia Sithole-Matarise)