Thompson held a meeting with senior staff to address the controversy that erupted a week ago, and has caused turmoil at the struggling Internet company and raised questions about his future as CEO.
Yahoo acknowledged last week that Thompson, the former president of eBay Inc division PayPal, does not have a computer science degree, despite what was stated in his official company biography and in regulatory filings with the U.S. Securities and Exchange Commission.
Thompson sent an email to Yahoo employees earlier this week apologizing for the controversy, and saying he hoped a Yahoo board review of the matter would be concluded promptly.
In the meeting on Thursday, Thompson gave an account of the facts as he understood them, the source said, and provided executives with an opportunity to ask questions.
Thompson's official biography at Paypal also listed the inaccurate education details, and it was unclear how Yahoo obtained the information on his educational record when it employed him.
Keith Giarman, who heads recruiting of top executives for venture capital and private equity firms at executive search firm DHR International, said high-level executives don't usually directly provide their resume to potential employers,
Typically, he said, a recruiting firm will compile a dossier about their client, which would include the client's resume and the firm's assessment of the candidate, and send it directly to companies.
Yahoo declined to comment on which executive search firm it used during its CEO search. According to past media reports, Yahoo used Heidrick & Struggles for its CEO search, but the firm did not present Thompson as a CEO candidate to Yahoo due to a conflict resulting from its work placing Thompson at PayPal.
Heidrick & Struggles was not immediately available for a comment.
The controversy comes as Yahoo is trying to revive its revenue growth and its popularity with consumers amid fierce competition from Google, Facebook and other online companies.
Since taking the reins, Thompson has moved fast to shake things up at Yahoo, laying off 14 percent of staff last month and filing a patent infringement suit against Facebook.
The discrepancy in his educational background was brought to light by activist hedge fund Third Point, which is Yahoo's largest outside shareholder and is waging a bitter proxy battle to install a slate of four directors on Yahoo's board.
Third Point has called for Thompson to be fired and for Yahoo to let one of its director candidates oversee the search for a new CEO.
Earlier this week, Yahoo's board appointed a special committee to investigate Thompson's background and to review the "facts and circumstances" surrounding his hiring.
Patti Hart, the Yahoo board member who oversaw the search committee that hired Thompson, announced that she would not seek re-election to Yahoo's board, saying she needed to focus on her role as CEO of International Game Technology.
Shares of Yahoo, which finished Thursday's regular trading session at $15.44, were down 4 cents in extended trading.
(Reporting By Alexei Oreskovic with additional reporting by Poornima Gupta; Editing by Andre Grenon and Richard Pullin)
By Alexei Oreskovic