Texas Gov. Rick Perry told CNBC on Monday that he doesn't "necessarily condone" what he referred to as the gay "lifestyle," nor does he "condemn it either."
Perry was responding to questions about comments he made last Wednesday in California, comparing homosexuality to alcoholism.
Earlier this month, the Texas Republican Party adopted at its convention a policy endorsing "reparative therapy" for gays and lesbians who seek to change sexual orientation through counseling.
Asked if he believes in that, Perry said in a "Squawk Box" interview: "I don't know. We'll leave that to the psychologists and the doctors."
The American Psychological Association has dismissed the idea that sexual orientation is a mental disorder, and has told its mental health professionals to avoid telling clients that they can change their sexual orientation.
The Republican governor, who's seen as possibly making another run at the GOP presidential nomination, said he wants to focus on states being able to make their own rules on single-sex marriage and other matters. "The idea that one size fits all coming out of Washington, D.C., is not going to work."
Texas has rejected the idea of gay marriage, and Perry said he respects that decision. But he added that he respects "what they want to do in California or New York" as well.
Last Tuesday, Perry arrived in the state capital of California—driving a Tesla Model S sedan and sending a message to Sacramento lawmakers that he means business when it comes to landing the electric car company's planned battery factory for Texas.
He told CNBC Monday: "For Tesla to go anywhere else, they'll be taking less of a deal, whether short-term or long-term, and [CEO] Elon Musk knows that. It's one of the reasons he's [also] looking to Texas to place his launch facility for SpaceX." That's the billionaire's commercial space venture.
Besides California and Texas—Nevada, Arizona, and New Mexico are also believed to be in the mix to get that Tesla battery plant, which would bring a $4 billion investment along with 6,500 manufacturing jobs.
Currently, Texas is among the states that prohibit Tesla from selling directly to consumers without using dealerships.
Would that change to get the Tesla factory? Perry told "Squawk Box" that "to lure companies you've got to be competitive ... so as the legislature comes back in January, my bet is they'll probably have that conversation."
Since Texas has the longest shared border with Mexico of any U.S. state, Perry has long been an advocate for tighter security, and he told CNBC Monday that it should be the top priority of immigration reform.
"We have been having that mantra with this administration for literally years," he said. The White House is "stonewalling Americans by not putting the resources on the border."
Asked whether the GOP's opposition to any kind of amnesty for illegal immigrants will turn off Hispanic voters, Perry said he's enjoyed their widespread support during his gubernatorial elections.
But in the last presidential election, his support for a policy to allow children of illegal immigrants to pay in-state tuition rates hurt his support among conservatives. He eventually dropped out the race.
More recently, immigration was seen as a major factor in House Majority leader Eric Cantor's primary loss last week to a tea party candidate. Shortly after the defeat, the Virginia Republican said he'd step down from his leadership position.
As for Perry, speculation about whether he'd make another run at the presidency started to intensify last year, when he said he would not seek a fourth term as governor. He's going to step down at the end of his current run next year.
—By CNBC's Matthew J. Belvedere. Reuters contributed to this report.