FRANKFURT (Reuters) - John Cryan, the chief executive of Deutsche Bank, said in a memo to staff on Wednesday he was "absolutely committed" to the lender, a day after Reuters and other news organizations reported the bank was searching for a new boss.

Two people familiar with the matter told Reuters on Tuesday that Germany's flagship bank had begun looking for a new CEO, as investors grow frustrated with the slow turnaround of the loss-making lender.

"Once again we are the subject of widespread rumours," Cryan said in the memo, posted on the bank's website. "I just wanted to reaffirm that I am absolutely committed to serving our bank and to continuing down the path on which we started some three years ago."

In his memo, Cryan said earnings "have so far not been what all of us would want them to be," but that the bank needed to stay on task.

"We need to focus on executing on the strategy that was agreed and signed off by both the management and supervisory boards. There is no difference of opinion here," he said.

The sources told Reuters that Paul Achleitner, chairman of the board, had initiated the search to replace Cryan, the British CEO who has been in office less than three years.

Cryan cited in the memo the recent initial public offering of the bank's asset management unit as "the obvious and most illustrative recent example of a key milestone of success."

Cryan has been criticized for falling behind in cutting costs. Deutsche Bank is conducting a global review of its investment bank that could result in cost cuts, a person with direct knowledge of the matter said on Wednesday.

(Reporting by Tom Sims; Editing by Victoria Bryan and Mark Potter)