(Bloomberg News) Bank of America Corp. Chief Executive Officer Brian T. Moynihan said he has no plans to step aside as head of the biggest U.S. lender.

"We're doing the right thing," Moynihan said today during an interview with CNBC. While the bank continues to build capital and may sell some businesses, Merrill Lynch units aren't likely to be among them because they're too important to customers, Moynihan said. He spoke after shares of the Charlotte, North Carolina-based company rose 17 percent, the best one-day showing since May 2009.

Moynihan, 51, assured employees in a memo yesterday that the bank is sound and getting control of costs tied to bad mortgages after shares of the lender plummeted 20 percent. While Moynihan has said the bank doesn't need to raise capital, analysts including Mike Mayo at Credit Agricole Securities USA say the idea can't be ruled out.

"The most important point to keep in mind is that our company remains financially strong -- in particular, much stronger than we were either during or coming out of the economic downturn of 2008-9," Moynihan wrote in his memo. "Most of the factors driving market volatility are beyond our control. But for matters within our control, we are taking action."

Bank of America advanced $1.09 to $7.60 a share as of 4 p.m. in today's New York Stock Exchange composite trading.

Moynihan is scheduled to speak again tomorrow in a public question-and-answer conference call hosted by mutual fund manager Bruce Berkowitz, whose Fairholme Capital Management LLC held 92.6 million Bank of America shares as of March 31. Berkowitz has promised to put the "toughest questions" about the bank's situation to Moynihan.