Also Read: Yellen Rejects Idea of Fed Audit

“Since those firms do pose systemic risk to the financial system, we should be making it tougher for them to compete and encouraging them to be smaller and less systemic,” she added.

“With respect to community banks,” Yellen continued. “We need a model for supervision of them that's different and much less onerous and has much less regulatory burden and is appropriate to their business model,” she said. “We are obviously imposing on the largest systemic institutions much higher and more onerous prudential standards.”

Heller also asked Yellen if she thinks the U.S. currently has a “safe and sound” financial system.

“We have a much safer and sounder financial system than we had pre-crisis, but as I indicated, I think we need to do more,” she responded.

“We are not at the end of the road in terms of putting in place regulations and enhanced supervision that will make the system safe and sound as it needs to be to contain systemic risk,” Yellen added.

Yellen also informed the committee that the Fed plans to raise capital standards further on large financial institutions.

“My assessment would be that we are making progress – that Dodd-Frank put into place an agenda that, as we complete it, should make a very meaningful difference in terms of 'too big to fail.' We've raised capital standards. We will raise capital standards further for the largest institutions that pose the greatest risk by proposing so-called SIFI capital surcharges,” she said.

“We have on the drawing boards the possibility of requiring that the largest banking organizations hold additional unsecured debt at the holding company level to make sure that they are capable of resolution,” she added.

Yellen stressed the importance of the federal government requiring banks to hold more capital.

“It's extremely important for our banks to have more capital, higher-quality capital. Basel III, putting those rules into effect has been an important step, and there are further steps that we will be taking with other regulators down the line to make sure that the most systemically important institutions, those whose failure could create financial distress, will be asked to hold more capital and … meet higher standards of liquidity and prudential supervision to make sure that they're more resilient,” Yellen said.

Under questioning from Sen. Bob Corker (R-Tenn.), Yellen told the committee she did not vote against any rate increases during her term on the Federal Reserve Board.

Yellen estimated that she voted in favor of rate increases 20 or more times.

“Twenty or more? I think it was maybe 27 or so,” Corker said.

“It could be,” Yellen replied.

Later in the hearing, she was pressed by Sen. Heidi Heitkamp (D-N.D.) to state the actual unemployment rate including individuals who have stopped looking for work or have part-time positions but prefer full-time work.

“The measured unemployment rate is 7.3%,” Yellen said.

“I know the measured unemployment rate, that wasn't the question,” said Heitkamp. “You would agree that it is at least close to or probably over 10%?” she asked.

“Well, certainly by broader measures it is that high,” said Yellen.

Current Fed Chair Ben Bernanke plans to step down at the end of January.