By Marti Maguire

RALEIGH, N.C. (Reuters) - North Carolina's Senate Republican leader on Wednesday filed a bill to repeal a controversial law on transgender restroom access while also clamping a temporary ban on cities from passing their own ordinances to protect transgender bathroom rights.

The compromise legislation filed by Senate President Phil Berger followed hours of closed-doors talks among Republicans, who were meeting in a special session to consider scrapping the law that has put North Carolina at the center of America's debate over transgender rights.

The state in March became the first to bar transgender people from using public restrooms that match their gender identity and pushback against the law helped spur Republican Governor Pat McCrory's re-election loss in November.

National protests and boycotts over the measure have been blamed for hundreds of millions of dollars in economic losses for North Carolina, as major sporting events such as the National Basketball Association All-Star Game were moved out of state.

Wednesday's special session was called to consider repealing the law known as House Bill 2, or HB 2, but action was delayed in both chambers, creating an air of uncertainty.

Republicans eventually proposed pairing a repeal with a six-month "cooling off period," in which local jurisdictions would be banned from enacting their own ordinances regulating public bathrooms, showers or changing facilities.

Critics of the law including transgender advocates cried foul over the cooling off period.

"This wasn't the deal," Democratic Senator Jeff Jackson said on Twitter, adding that the Republican Party had "broken its promise."

Transgender rights advocates were outraged.

"Don't be fooled: this is not full repeal of HB 2, (it) doubles down on discrimination, and makes clear that NC is still closed for business," said Chad Griffin, president of the Washington-based Human Rights Campaign.

HB 2 was enacted largely in response to a local measure in Charlotte that protected the rights transgender people to use public bathrooms of their choice. The Charlotte City Council on Monday repealed its ordinance as a prelude to the state repealing HB 2.

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Democratic Governor-elect Roy Cooper, a fierce critic of the bathroom restrictions who campaigned on repealing them, said he had received Republican assurances about repealing HB 2 after Charlotte rescinded its ordinance.

But in the state House of Representatives, some Republicans protested the session being called at all, saying they would vote against any measure proposed. The law remains popular among social conservatives in rural areas of the state.

Addressing the Senate, Berger said his bill was designed to "take the state back to the status quo that existed before Charlotte passed its ordinance. "It gives everyone a chance to start over," he said.

(Writing by Letitia Stein and Daniel Trotta; Additional reporting by David Ingram; Editing by Bill Trott and Tom Brown)