WASHINGTON — During the 2008 financial crisis, Neel Kashkari worked tirelessly to save the nation’s largest banks. As a senior Treasury Department official in the George W. Bush and Obama administrations, he helped those banks grow larger than ever.

On Tuesday, he said it was time to think about breaking them up.

“I believe the biggest banks are still too big to fail and continue to pose a significant, ongoing risk to our economy,” Mr. Kashkari said at the Brookings Institution, delivering his first public speech as the new president of the Federal Reserve Bank of Minneapolis.

He described the threat of another crisis that might force the government to bail out large banks, as it did in 2008, as a rare instance of a clear and preventable problem.

“The question is whether we as a country have the courage to actually take action now,” he said.

Mr. Kashkari’s remarks caused a stir in Washington. Such views have become relatively common at both ends of the political spectrum — providing fuel for the presidential campaigns of Senator Bernie Sanders, Democrat of Vermont, and Donald Trump, a Republican — but Mr. Kashkari is a moderate Republican and a former employee of Goldman Sachs.