The Federal Reserve’s newest bank president, a Republican who served as a top Treasury Department official during the financial crisis, called Tuesday for policy makers to consider breaking up big banks to prevent future government bailouts.

In his first public remarks since taking over as chief of the Federal Reserve Bank of Minneapolis in January, Neel Kashkari said efforts to rein in the banks through the 2010 Dodd-Frank law “did not go far enough.”

The law hasn’t ended the problem of banks so big that their collapse would endanger the financial system and economy, forcing the government to rescue them in a crisis, he said, referring to institutions considered “too big to fail.” In response, Mr. Kashkari, who served in the administration of President George W. Bush, said policy makers must “give serious consideration to a range of options,“ including, “breaking up large banks into smaller, less connected, less important entities,” regulating them like a public utility or “taxing leverage throughout the financial system to reduce systemic risks wherever they lie.”

His remarks come during a heated presidential primary season in which candidates of both parties are assessing the lessons of the financial crisis. Democratic presidential candidate Sen. Bernie Sanders has been firing up audiences by attacking what he calls Wall Street’s greed, while several GOP candidates have criticized Dodd-Frank and said it hasn’t ended the problem of too-big-to-fail firms.

“The financial sector has lobbied hard to preserve its current structure and thrown up endless objections to fundamental change,” Mr. Kashkari said at the Brookings Institution in Washington. “And in the immediate aftermath of the crisis, when the Dodd-Frank Act was passed, the economic outlook was perhaps too uncertain to take truly bold action. But the economy is stronger now, and the time has come to move past parochial interests.”