Later in a telephone interview, he said he did not regret any policy positions he took while running for president and denied that he was walking back his comments about assault weapons. He said that as governor, he would push for universal background checks and requirements for the safe storage of firearms.

“I don’t think that we should have AR-15s and AK-47s on the streets of this state — I have seen what they do to my fellow Texans in El Paso in 2019,” he said, referring to a mass shooter who killed 23 people at a Walmart in the deadliest anti-Latino attack in modern American history. “I haven’t changed a thing about that. I’m just telling you I’m going to focus on what I can actually do as governor and where the common ground is.”

Mr. O’Rourke’s predicament illustrates how hard it can be for a red-state Democrat to return to local politics after running for federal office in the national spotlight. What appeals to voters in a crowded Democratic primary for president may turn off those in a statewide race back home in a Republican-dominated state.