"I am in no position to judge the competence of the investigation and should never have done so," he said in the letter. "My own lay view is that it has been more than thorough, indeed it has in some respects appeared to be excessive."
Murdoch pointed to employees who were arrested in 2012, early in the investigation, and "are still in limbo" awaiting charging decisions from prosecutors.
"This has gone on too long," he said, questioning whether police have approached the investigation "with an appropriate sense of proportion" or with regard to the human costs of delay.
The recording allegedly made secretly when Murdoch addressed staffers from The Sun newspaper back in March made waves in Britain because it appeared to be at odds with Murdoch's vigorous public condemnations of illegal behavior at his newspaper titles.
Scotland Yard had previously said it is seeking a copy of the recording with an eye toward "assessing the full contents of that tape."