Billionaire investor Warren Buffett told CNBC that he stands by his support of Wells Fargo CEO Tim Sloan, after backing the beleaguered chief executive minutes before Sloan's resignation was announced.

Buffett initially said he supported Sloan "100 percent" in an interview Thursday with CNBC's Becky Quick at The Gatehouse's Hands Up for Success luncheon in Grapevine, Texas. "I don't want his job. ... I'm very empathetic to anybody who walks into a big problem and a very, very large and politically sensitive institution," Buffett said.

The investor later told CNBC that he knew Wednesday that Sloan planned to resign. Buffett said Sloan called him Wednesday wanting to know if he could talk the next day, but Buffett told him he was going to be out of the office all day and so Sloan told him the news. Buffett said that the move was "out of the blue" and that he had not spoken to anyone on the Wells Fargo board about it.

Buffett's Berkshire Hathaway is the bank's single-largest shareholder.

Sloan is resigning as CEO immediately, Wells Fargo said Thursday in a release shortly after Buffett made his remarks. The bank's general counsel, Allen Parker, will take over as interim chief executive, and Wells Fargo is searching externally for a permanent successor. Sloan was supposed to clean up the mess that had claimed his predecessor, but had struggled to satisfy regulators' demands to overhaul the sprawling institution.

—CNBC's Hugh Son contributed to this report.