WASHINGTON (CNN) -- Jeb Bush signaled an increasing openness to same-sex marriage calling for "respect for the good people" on all sides of the issue in a statement he released on Monday.

His statement comes as Florida, where he spent eight years as the Republican governor, begins allowing same-sex marriages after a judge -- following similar rulings across the nation -- struck down the state's old law banning such unions.

"We live in a democracy, and regardless of our disagreements, we have to respect the rule of law," Bush said.

"I hope that we can also show respect for the good people on all sides of the gay and lesbian marriage issue -- including couples making lifetime commitments to each other who are seeking greater legal protections and those of us who believe marriage is a sacrament and want to safeguard religious liberty," he said in the statement provided to CNN by an aide.

Bush's comment comes after telling The Miami Herald over the weekend that decisions on whether to allow same-sex marriages should be left to individual states.

Long an opponent of same-sex marriage, Bush once struck a much harsher tone on the issue.

"We have enough special categories, enough victims, without creating even more," he wrote in a 1994 opinion piece in The Miami Herald.

He wrote that he didn't want to see "sodomy be elevated to the same constitutional status as race and religion."

Democratic National Committee spokesman Mo Elleithee said he isn't buying that Bush's position has evolved.

"It took Jeb Bush 69 words to say absolutely nothing -- 69 words not to say, 'I support marriage equality.' Nothing's changed," Elleithee said.

"At the end of Bush's statement, he still had the same position: He opposes the right of gay and lesbian Floridians -- and all LGBT Americans -- to get married and adopt children," he said. "If he wants to tell us he's changed his position, great. But this was not that statement. It was typical Jeb Bush."

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