WASHINGTON — Defense Secretary Chuck Hagel wants military leaders to inject more urgency into ensuring “moral character and moral courage” in a force suffering a rash of ethical lapses.

Hagel has been worried by a string of scandals that has produced a wave of unwelcome publicity for the military. But in light of new disclosures this week, including the announcement of alleged cheating among senior sailors in the nuclear Navy, Hagel on Wednesday demanded a fuller accounting of the depth of the problem.

Last month the Air Force revealed it was investigating widespread cheating on proficiency tests among nuclear missile launch officers in Montana, and numerous senior officers in all branches of the armed forces have been caught in embarrassing episodes of personal misbehavior, inside and outside the nuclear force. The Air Force also is pursuing a drug use investigation, and a massive bribery case in California has ensnared six Navy officers so far.

At the same time, hundreds of soldiers and others are under criminal investigation in what the Army describes as a widespread scheme to take fraudulent payments and kickbacks from a National Guard recruiting program.

The steady drumbeat of one military ethics scandal after another has caused many to conclude that the misbehavior reflects more than routine lapses.