Big banks should not be allowed to dip into FDIC-insured deposits to engage in risky trading activities, Sen. Elizabeth Warren told CNBC on Friday as she pushed for a new, modern-day bank breakup bill.

"There is no single magic bullet to stop 'too big to fail,'" the Massachusetts Democrat said in a "Squawk Box" interview. "But the central premise behind a 21st century Glass-Steagall is to say, 'If you want to get out there and take risks, go and do it. But what you can't do is you can't get access to FDIC-insured deposits when you do.'"

Warren, along with Sens. John McCain, R-Ariz., Maria Cantwell, D-Wash., and Angus King, I-Maine, have introduced legislation to separate traditional banks that have savings and checking accounts from riskier financial institutions that offer services such as investment banking, insurance, swaps dealing, and hedge fund and private equity activities.

(Read More: Warren Pushing Bill to Break Up Big Banks)

"[The bill] helps bring down the size of some of the financial institutions," Warren, a member of the Senate Banking Committee, said. "And it says, 'At least one portion of our banking sectors stays safer.'"

After the 2008 financial crisis, there were calls to bring back Glass-Steagall, the law that had separated depository banks from investment banks following the 1929 crash. It was repealed in 1999.