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HOUSTON – Houston Mayor Annise Parker said Monday her election to lead the nation’s fourth-largest city marked a milestone for gay Americans but was just “one step toward a tomorrow of greater justice.”

Parker was sworn in over the weekend in a private ceremony and repeated her oath during a public ceremony Monday. Her partner, Kathy Hubbard, held a Bible that belonged to Parker’s grandparents for the swearing-in by U.S. District Judge Vanessa Gilmore.

Parker took almost 54 percent of the vote in a runoff last month, defeating former city attorney Gene Locke in a race to succeed Bill White, who had reached his term limit. Her election made Houston the largest U.S. city to elect an openly gay mayor.

“I spoke on election night of that being an historic election, and my election made news all around the world,” she told the more than 1,000 people who gathered at the city’s Wortham Theater. “Now, Houstonians weren’t very surprised they elected a gay woman. We have a tradition of electing mayors not for who they are but for what they believe we can do as a city.”

The three-term former city controller has never made a secret or issue of her sexual orientation in any of her runs for office. But she was criticized because of her sexual orientation by anti-gay activists and some religious groups, who endorsed Locke and sent out mailers condemning her.

Parker addressed some of her inaugural remarks to the city’s gay, lesbian, bisexual and transgender community specifically.

“I understand how much this day means to you,” she said. “I can feel your excitement and your joy.”

But she said she also could feel their “apprehension and your longing for acceptance.”

“Your bravery in the face of threat, your grace in the face of insult, sustains me,” she said. “I will gladly carry you forward.

“But today is simply one step toward a tomorrow of greater justice.”

Several smaller U.S. cities, including Portland, Ore., Providence, R.I., and Cambridge, Mass., have openly gay mayors.

Gay and lesbian rights organizations from across the country endorsed Parker and contributed money to her campaign and staged get-out-the-vote phone banks.

Several demonstrators gathered outside the theater Monday, with pro-gay activists outnumbering anti-gay.

Parker worked for two decades in the oil and gas business, specializing in economic modeling, and began her political career as a gay activist. After two unsuccessful tries, she won a city council seat in 1997, was re-elected twice, then won three terms as city controller before winning the mayor’s job.

She’s Houston second female mayor. Kathy Whitmire, who also served as city controller, was elected in 1981 and was re-elected four more times before losing in 1991.

Parker takes over a city of 2.2 million that’s weathered the national recession better than most but still is facing what she’s estimated as a budget deficit of about $3 million.

“Every speech by every mayor in this country these days will discuss the economic downturn,” she said Monday. “In truth, the quality of life in many cities is not what it was four years ago.

While acknowledging a budget shortfall, “We will not let that happen to the city of Houston,” she said.

Parker inherits unfunded pension-fund commitments for police, firefighters and other city workers, sagging revenues from water and sewer operations that may require rate increases, and a campaign promise to overhaul the police department whose chief quit last week and whose largest union representing officers endorsed Locke. She’ll also need to replace the chairman of the board that oversees Metro, the city’s public transit agency.

Her predecessor, White, announced last year he was a candidate for the U.S. Senate, then last month abandoned that bid to seek the Democratic nomination for governor.

Parker’s victory last month came after several setbacks for gay rights activists. New York lawmakers in December rejected a bill that would have made their state the sixth to allow marriage between same-sex couples. In November, Maine voters repealed their legislature’s passage of a state law allowing same-sex marriage. California briefly allowed gay marriage before a public vote in 2008 banned it. And the New Jersey Legislature, which had been working on a same-sex marriage bill, postponed a recent vote when the measure appeared headed for defeat.

In the District of Columbia, however, the city council last month passed and the mayor signed a measure allowing same-sex marriage, although it still needs to gain Congressional approval. And with the new year, New Hampshire joined Massachusetts, Vermont, Connecticut and Iowa in allowing gay marriage.

Also Monday, former Georgia state Sen. Kasim Reed was sworn into office as Atlanta’s 59th mayor. Reed overcame low early poll numbers to win a runoff over city councilwoman Mary Norwood, who was trying to become the mostly black city’s first white mayor in a generation.