Federal Reserve Chair Janet Yellen sought to reassure worried lawmakers on Thursday that when the Fed begins to raise interest rates, it will be careful not to derail the economy.

Delivering her second day of congressional testimony, Yellen responded to concerns from some Democratic senators that once the Fed does start raising rates, it could set back job market and income gains.

Both Sens. Robert Menendez, D-New Jersey, and Charles Schumer, D-New York, told Yellen that with inflation at such low levels now, it would be a mistake for the Fed to begin raising interest rates too quickly. The more prudent course, they said, would be to keep rates low and give the labor market more time to heal from the Great Recession.

Yellen said the Fed was facing a delicate balancing act in achieving its dual goals of achieving maximum employment and stable prices.

"We don't want to cut off job growth and income growth, and we do want to see inflation move up to 2 percent," Yellen said. "We would not be pleased to see it linger indefinitely below 2 percent."

In an appearance before the Senate Banking Committee, Yellen reiterated her view that if the economy keeps improving, the Fed will likely begin raising rates this year. The Fed has kept its benchmark rate at a record low near zero since December 2008, and it has been nine years since it has actually raised the federal funds rate.

Yellen said that the Fed wants to see further improvement in the labor market and have greater confidence that inflation is moving back toward its 2 percent target before it starts raising rates.

Yellen's appearance before the Senate panel was less confrontational than her appearance Wednesday before the House Financial Services Committee.

Before the House panel, a number of Republican lawmakers took Yellen to task for refusing to turn over documents the House panel subpoenaed. The documents are connected to an investigation of a possible Fed leak of market-sensitive information in October 2012. Yellen has said she was withholding some documents upon the advice of the Fed inspector general that turning the material over could jeopardize an on-going investigation.

Members of the Senate panel did not bring up the leak investigation. Republican lawmakers in both the House and Senate are sponsoring legislation aimed at making the Fed more accountable to Congress. Yellen repeated comments she had made before the House panel that the Fed is already among the most transparent central banks in the world and urged Congress not to make changes that could undermine the Fed's ability to conduct monetary policy.

On monetary policy, Yellen said that she did not believe the Fed is overly influenced by concerns about financial markets.

"We can't completely ignore what is happening in the markets," she said. "It is one element of our evaluation, but I don't think we pay undue attention to it."

Sen. Elizabeth Warren, D-Massachusetts, pushed Yellen to be tougher in reviewing the "living wills" that the nation's large banks are now required to submit each year. The wills detail to regulators how they could be shut down in the event they become insolvent.

These wills were required in the 2010 overhaul of financial regulations aimed at avoiding a repeat of the 2008 financial crisis. But Warren and others have complained that regulators have not been tough enough in enforcing this provision of the overhaul law.

Yellen told Warren that if the living wills the banks submit are not adequate "we are certainly prepared to say they are not credible."