Despite last week's landmark U.S. Supreme Court ruling requiring states to allow same-sex marriage, Paxton says it "did not diminish, overrule, or call into question the First Amendment rights to free exercise of religion."

Paxton said the Supreme Court "fabricated a new constitutional right."

"This newly invented federal constitutional right to same-sex marriage should peaceably coexist alongside longstanding constitutional and statutory rights, including the rights to free exercise of religion and speech," he said.

The Supreme Court’s ruling has sparked controversy ranging from religious freedom to how parents should talk to children. CBN's Heather Sells spoke with Dr. Russell Moore, with the Southern Baptist Convention’s Ethics and Religious Liberty Commission, on these topics and more fallout on the historic ruling. - http://www.cbn.com/cbnnews/Video-embeds/2015/June/Gay-M arriage-What-Now-for-Christians-and-the-Church/ - Watch Video

Paxton noted that officials who refuse to issue marriage licenses to gay couples could face litigation and/or fines. But he added that "numerous lawyers stand ready to assist clerks defending their religious beliefs, in many cases on a pro-bono basis."

"And I will do everything I can from this office to be a public voice for those standing in defense of their rights," he said.

In Kentucky, some clerks are refusing to issue marriage licenses to any couples as an objection to the U.S. Supreme Court's ruling on same-sex marriage.

Is the debate over gay marriage in America over? What will happen to religious individuals and institutions who continue to stand for traditional marriage? Peter Sprigg, with the Family Research Council, explains. - http://www.cbn.com/cbnnews/Video-embeds/2015/June/Is-th e-Gay-Marriage-Debate-over-in-America/ - Watch Video

Casey County Clerk Casey Davis said his religious convictions will not allow him to issue marriage licenses to same-sex couples. He said his office is no longer issuing licenses to any couple.

"In good conscience I cannot put my name on one of those licenses," he said.

Davis said no same-sex couple has been in to the office to ask for one. The Lexington Herald-Leader reported that clerks in Rowan and Lawrence counties have also halted issuing marriage licenses in response to the Supreme Court ruling.

Terry Sebastian, a spokesman for Gov. Steve Beshear, said the governor's office is reviewing how to respond.

Meanwhile, pastors around the country are trying to figure out what to do if homosexuals asked to be married in their churches.

One large church in San Jose, California – the Jubilee Christian Center – temporarily suspended all weddings.

"I am not a religious bigot.  I've been called worse," Jubilee Pastor Dick Bernal said. "I'm a Bible believing person, and I would hope people would respect Dick Bernal believes the Bible, and I'm not going to violate his beliefs."

Pastor Bernal says some members of his church are gay, but he will not perform gay marriages.

Other churches and denominations have already taken steps to embrace homosexuality. The Episcopal Church is voting Wednesday on whether to allow religious weddings for same-sex couples.