WASHINGTON, Jan 13 (Reuters) - Morgan Stanley will pay $13 million to settle civil charges that it overbilled some of its wealth management clients because of coding and other billing system errors, U.S. regulators said Friday.

The Securities and Exchange Commission said the bank was also charged with violating custody rules designed to safeguard investor assets. The bank agreed to settle the case without admitting or denying the charges. (Reporting by Sarah N. Lynch; Editing by Jonathan Oatis)