President Barack Obama has said that religious freedom is not a valid reason to deny any American their constitutional rights and argued that traditional marriage supporters simply need to "catch up" to the rest of the country.

"We affirm that we cherish our religious freedom and are profoundly respectful of religious traditions," he said during a speech given at a Democratic National Committee LGBT fundraising gala in New York City on Sunday night.

However, Obama charged that "our religious freedom doesn't grant us the freedom to deny our fellow Americans their constitutional rights."

According to a report from Fox News, Obama claimed that his administration was respecting what he described as "genuine concerns" of religious institutions and touted the progress made on gay rights under his administration.

He also contended just as they did in 2004, Republicans are exploiting the issue to earn more votes.

"The good news is they probably won't use marriage equality as a wedge issue like they did in 2004 because the country has come too far," he said of GOP candidates, including Ben Carson, Ted Cruz and Mike Huckabee. "In fact, America has left the leaders of the Republican Party behind."

The president also asserted that he will not back down in his efforts to make progress for the LGBT community despite opposition: "What makes America special is, is that though sometimes we zig and zag, eventually hope wins out," he said, explaining it would take time for gay marriage opponents to "catch up" to the rest of the U.S.

"But it only wins out because folks like you put your shoulder behind the wheel and push it in that direction," he said.

The president's comments come just weeks after Kentucky clerk Davis spent several days in jail because she refused to issue marriage licenses to gay couples.

At the time, Davis explained that the U.S. Supreme Court's ruling on June 26 that legalized gay marriage nationwide conflicts with the vows she made when she became a born-again Christian.

"I promised to love Him with all my heart, mind and soul because I wanted to make heaven my home," Davis said. "God's moral law conflicts with my job duties. You can't be separated from something that's in your heart and in your soul."

"I am no hero. I'm just a person that's been transformed by the grace of God, who wants to work, be with my family. I just want to serve my neighbors quietly without violating my conscience," the clerk added.

While Davis received support from many Christian and conservative leaders, an ABC News/Washington Post poll earlier in September found that the majority of Americans believe that she should indeed be required by law to issue licenses to gay couples.

The survey further found that 74 percent of respondents believe that equality under the law is more important than religious freedom when the two collide, and 72 percent backed the decision to send Davis to jail for failing to comply with the order.