LONDON (Reuters) - Lloyds Banking Group <LLOY.L> Chief Executive Antonio Horta-Osorio apologized to staff on Wednesday for damaging the bank's reputation but said he intended to continue running the British lender following press scrutiny of his private life.

In a memo to employees seen by Reuters, Horta-Osorio addressed a report by the The Sun newspaper earlier this month that said the married chief executive ran up a 3,826 pound ($4,962) hotel bill while spending time with another woman.

"My personal life is obviously a private matter as it is for anyone else. But I deeply regret being the cause of so much adverse publicity and the damage that has been done to the Group's reputation," Horta-Osorio wrote in the memo.

The tabloid story alleged Horta-Osorio had improperly claimed the personal spending as a business expense, but the executive said in the memo the bank had cleared him of any wrongdoing regarding his expenses.

Lloyds has said its Chairman Norman Blackwell had reviewed the allegations and was also satisfied Horta-Osório had paid his own personal expenses while attending a Singapore conference.

The Lloyds chief executive, who is Portuguese, has run the bank for the past five years and is highly regarded for turning around the lender after it struggled following the financial crisis.

Top investors in the bank had expressed concerns Horta-Osório might leave sooner than anticipated following the press scrutiny.

"... please be assured that I am as committed as ever to leading the Group forward to deliver our strategy and to meet our future ambitions," Horta-Osorio said in the memo on Wednesday.

(Reporting by Lawrence White Editing by Sinead Cruise and Mark Potter)