Sen. Warren: No risky trading with insured deposits

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 It was repealed in 1999.

"Let's remember why we're here," bank analyst Christopher Whalen said on "Squawk Box" earlier Friday. "The Fed allowed the dismantlement of Glass-Steagall, and they allowed the creation of this ghetto we call the over-the-counter derivative market because core-banking wasn't profitable."

The 2010 Dodd-Frank Wall Street Reform law stopped short of breaking up the banks in favor of reigning-in risk-taking.

While a Warren-like law would restrict the big banks, Whalen of Carrington Investment Services argued that "dealing with a narrow bank that just lent money ... would probably be cheaper."

The reason, he added, "There is a premium in terms of getting credit from the big houses because of their volatile activities."

Last summer, former Citigroup Chairman and CEO Sandy Weill dropped a bomb on the financial industry during an appearance on "Squawk Box," when he said it was time to breakup the megabanks that he helped create.

(Flashback: Wall Street Legend Sandy Weill: Break Up the Big Banks)

But former Wells Fargo Chairman and CEO Richard Kovacevich disagreed strongly on Friday with Weill and the Warren-approach.

"It's very misguided," Kovacevich told CNBC before Warren's interview, arguing that "'plain vanilla' investment banking is probably the least risky of all financial products—far less risky than consumer lending or commercial lending."

He said the financial crisis happened "because we gave the exclusivity to the capital markets to ... investments banks who used the profits from that to then do a lot of proprietary trading."

Kovacevich also insisted there's no relationship between the size of a bank and risk. "Let's go back to the S&Ls. None of those were big in the 1980s, and they all failed."

But Warren's counter to that argument is that banks have kept on getting bigger over the years, and as a result the government had to "bail them out when they got into big financial trouble."

She acknowledges that her bill does not pretend to fix everything, but it "moves us in the right direction."

—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.