WASHINGTON — The Senate took a key step on Tuesday toward loosening rules imposed after the 2008 financial crisis as some Democrats joined with Republicans to vote to begin debate on legislation that would roll back restrictions on large parts of the banking industry.

In a rare demonstration of bipartisanship, the Senate voted 67 to 32 to allow the bill to proceed, setting the stage for a vote this week that rewrites parts of the 2010 Dodd-Frank Act.

While the bill is intended to provide relief to thousands of small and midsize banks, the prospect of deregulating the financial industry has laid bare a fissure in the Democratic Party, pitting moderate Democrats who support easing bank rules against progressives who view the bill as a gift to Wall Street.

“This deregulatory bill puts the entire economy at risk,” Senator Elizabeth Warren, Democrat of Massachusetts, said on Tuesday. “We’re not here to do the bidding of Wall Street banks. We’re here to do the bidding of the American people.”