Yahoo CEO Scott Thompson says he's sorry, but he's not admitting any wrongdoing.

Thompson, under heavy fire for a discrepancy in his resume, sent an apology via email to company employees for the tumult that has embroiled Yahoo for nearly a week now.

The new CEO, however, did not say he was stepping down, and did not address the issue of his resume.

"As I told you on Friday, the board is reviewing the issue, and I will provide whatever they need from me," Thompson wrote in the memo, which was reprinted by the Financial Times.

"In the meantime, I want you to know how deeply I regret how this issue has affected the company and all of you. We have all been working very hard to move the company forward, and this has had the opposite effect. For that, I take full responsibility, and I want to apologize to you," he added.

Yahoo's board has been looking into the issue but has not yet announced what, if any, actions it will take.

Demands for Thompson's ouster started last week after Yahoo disclosed that its board is investigating the resume discrepancy. The company has acknowledged that both Thompson's resume and Yahoo's regulatory filings with the U.S. Securities and Exchange Commission overstated his technology background to include a degree in computer science that he does not have.

The company called it "an inadvertent error."

The board's investigation has prompted a very public debate over Thompson's ability to continue to lead the struggling company.

Daniel Loeb, CEO of Third Point LLC, one of Yahoo's largest investors and the man who reported the discrepancy in Thompson's resume to the SEC, was the first to pressure the company to take action against Thompson.

On Monday, Third Point sent a letter calling on Yahoo executives to reveal all documents related to Thompson's interviews and hiring. The hedge fund also asked for documents related to the appointment of several board members.

"Third Point believes that Yahoo shareholders and employees will be best served if the Board accepts responsibility quickly for this latest debacle," Third Point said in a statement. "We believe that this internal investigation by this board must not be conducted behind a veil of secrecy and shareholders deserve total transparency."

Late last week, Eric Jackson, founder of Ironfire Capital, which reportedly owns about 3.2 million Yahoo shares, said in an interview with the San Jose Mercury News that it's time for Thompson to be replaced.

Industry analysts generally agree that this very public row over the accuracy of Thompson's resume, as well as his integrity, has left his reign at Yahoo tenuous at best.

And that could spell trouble for a once high-flying Internet pioneer that has struggled in recent years.

Thompson, who gained the CEO seat early this year, has adopted a take-no-prisoners philosophy to leading the company, overseeing layoffs and the ouster of Yahoo board members, analysts noted.

Sharon Gaudin covers the Internet and Web 2.0, emerging technologies, and desktop and laptop chips for Computerworld. Follow Sharon on Twitter at @sgaudin, or subscribe to Sharon's RSS feed . Her e-mail address is sgaudin@computerworld.com.