FORT BLISS, Texas—Former Democratic Rep. Beto O’Rourke, weighing a presidential bid, distanced himself from the Democratic socialist movement in his party’s left wing and championed free-market forces to achieve progressive policy goals.

“I’m a capitalist. I don’t see how we’re able to meet any of the fundamental challenges that we have as a country without, in part, harnessing the power of the market,” the 46-year-old told reporters at an Army base in El Paso, which he had represented in Congress. “Climate change is the most...