NEW YORK (CNN/Money) - One of the most closely watched speeches of President Bush's administration is scheduled Tuesday as the former Texas oilman addresses concerns about corporate governance and his Wall Street watchdog.

The speech, at a hotel in New York's Financial District, comes amid weakness in the U.S. stock markets as company after company reveals accounting problems totaling billions of dollars.

Bush is widely expected to reiterate proposals for corporate governance that he and other members of his administration already have made, including a requirement that executives certify their financial statements are correct and be prosecuted criminally if they are misleading.

Treasury Secretary Paul O'Neill on Tuesday underlined the potential punishment for corporate leaders. "We've got to make it much clearer for them because we're going to put people who abuse their authority and hurt shareholders and employees in jail where they belong," he told NBC's "Today." (details)

The president may also use the opportunity to again defend Securities and Exchange Commission Chairman Harvey Pitt. Sens. Tom Daschle, D-S.D., and John McCain, R-Ariz., have called for Pitt to resign, calls Bush rejected Monday. (More)

"I support Harvey Pitt," said Bush, who noted that Pitt was unanimously approved by the Senate. "Every senator said 'aye' on Harvey Pitt, meaning they thought he was the right man for job. I still think he is."

Pitt has been criticized for his prior employment by lobbyists for the very accounting industry he now regulates, and critics have said he's moved too slowly to respond to accounting scandals surrounding Enron Corp., Global Crossing Ltd., WorldCom and other companies.

Bush on Monday called criticism of his past business deals nothing more than political attacks, while across the Mall in Washington the latest accounting scandal dogging Corporate America took center stage on Capitol Hill. (Allegations)

The president used a hastily called, 35-minute news conference at the White House to deny yet again that he did anything wrong when he sold stock in Harken Energy Corp. more than a decade ago.

"People are going to attack me based on Harken,'' he said. "That's nothing new. This is recycled stuff," the president told reporters. (Click here for more)

Bush's news conference came as worries about corporate accounting and possible fraud by top executives have driven stock prices sharply lower in recent weeks -- creating a potential crisis of confidence in America's financial markets that could undermine the country's fledgling economic recovery.

Bush sat on Harken's board of directors in the late 1980s and early 1990s and sold a block of stock shortly before the company reported a large loss that drove down its stock price. The White House said last week that a "mix-up" by lawyers at Harken was to blame for Bush's delay in filing reports on stock transactions worth more than $1 million before he was elected governor of Texas. (More)

Meanwhile, on Capitol Hill, executives of WorldCom Inc. blamed the company's accounting firm, Arthur Andersen, and its former chief financial officer for the missteps that forced it to admit last month that it overstated pretax profits by at least $3.8 billion.

The two former executives who led WorldCom at the time it overstated profits -- former CEO Bernard Ebbers and Scott Sullivan, fired as WorldCom's chief financial officer on the day it dropped its accounting bombshell -- declined to testify at a hearing before a House panel. (Key players in WorldCom hearings)

Their silence provoked outrage from lawmakers on the House Financial Services Committee who were investigating the biggest accounting scandal yet -- one that cost investors billions of dollars and may yet force the nation's No. 2 long-distance phone company into bankruptcy. (More)

On Wall Street, U.S. stock prices fell sharply in response to news of accounting irregularities at Merck & Co. (MRK: Research, Estimates) -- a blue-chip drugmaker and just the latest bad news from Corporate America. (More)

Even as Bush and members of his administration have toughened their rhetoric about corporate responsibility, the president has faced tough questions about his sale of stock associated with Harken Energy.

Questions have also been raised about Vice President Dick Cheney's role at Halliburton (HAL: Research, Estimates), the oilfield services company being investigated by the SEC for its accounting practices under Cheney, who was the company's CEO from 1995 to 2000. (More)

Back on Capitol Hill, a congressional panel called on the boards of 13 troubled U.S. companies to hand over records of their management oversight and expanded an earlier request seeking SEC records.

The House Energy and Commerce Committee demanded records from the boards of WorldCom, Enron, Xerox, Tyco International, Kmart Corp. and nine other firms. (More)

For its part, WorldCom sued its fired CFO Sullivan, seeking the return of a $10 million bonus it paid him, Reuters news agency reported, citing a copy of the lawsuit obtained Monday.

Sullivan and his lawyer were not immediately available for comment because they were at a congressional hearing probing the WorldCom scandal. (More)

Elsewhere, the Business Roundtable, a group of chief executive officers of major corporations, endorsed the SEC's new rule requiring top corporate officials to certify financial statements are accurate, as well as congressional legislation to tighten oversight of the accounting industry.