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Senator Bernie Sanders, Independent of Vermont and a 2016 Democratic candidate for president, is pushing his new role as a voice to the left of Hillary Rodham Clinton.

On Wednesday, despite refusing to answer any questions about his Democratic rival, Mr. Sanders offered yet another glimpse at the sort of populist issues he planned to inject into the Democratic nominating fight.

“Today, 99 percent of all new income is going to the top 1 percent,” Mr. Sanders said in a news conference in the Capitol to introduce legislation that would break up the banks that are deemed “too big to fail.”

“The top one-tenth of 1 percent now owns almost as much wealth as the bottom 90 percent,” he said.

Mrs. Clinton has come under fire for her family’s close ties to the financial sector, including highly paid speeches made for Wall Street bankers.

Mr. Sanders’s legislation, which he introduced with Representative Brad Sherman, Democrat of California, would require regulators at the Financial Stability Oversight Council to establish a list of banks that are “too big to fail” — and then call on the Treasury secretary to break up those financial institutions within a year.

“If an institution is too big to fail, it is too big to exist, and that is the bottom line,” Mr. Sanders said.

