The manufacturer said it had found debris inside wing fuel tanks of aircraft that have not yet been delivered to customers.
Boeing said the discoveries were “absolutely unacceptable”, but added the new issue would not affect the aircraft’s expected return to service later this year.
Tui Airways, which has 15 Max aircraft, has already factored in replacements for the rest of this year.
Boeing has also appointed an executive to oversee the Max issue.
Mike Fleming becomes vice-president, Boeing 737 Max return to service and global aviation safety system.