WASHINGTON — Concerned that ethical problems inside the military might run deeper than he realized, Defense Secretary Chuck Hagel ordered service leaders Wednesday to add urgency to their drive to ensure “moral character and moral courage” in a force emerging from more than a decade of war.

Almost a year into his tenure as Pentagon chief, Hagel had been worried by a string of ethics scandals that 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 decided to push for a fuller accounting.

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.

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.

“He definitely sees this as a growing problem,” Hagel’s chief spokesman, Navy Rear Adm. John Kirby, told a Pentagon news conference Wednesday after Hagel met privately with the top uniformed and civilian officials of the Army, Navy, Air Force and Marine Corps.

“And he’s concerned about the depth of it,” Kirby said. “I don’t think he could stand here and tell you that he has — that anybody has — the full grasp here, and that’s what worries (Hagel) is that maybe he doesn’t have the full grasp of the depth of the issue, and he wants to better understand it.”

Hagel’s predecessor, Leon Panetta, had launched an effort to crack down on ethics failures more than a year ago, and the matter has been a top priority for the chairman of the Joint Chiefs of Staff, Gen. Martin Dempsey, for even longer.

Kirby said Hagel has come to realize that he needs to investigate as well.

“We don’t fully know right now what we’re grappling with here and how deep and serious it is,” Kirby said. “And I think, you know, for a leader at his level with the responsibilities that he carries every day, not knowing something like that is something to be concerned about. And he wants to know more.”

Hagel believes that the vast majority of military members are “brave, upright and honest,” and he is encouraged by efforts already under way to curb misconduct, including sexual assaults, Kirby said.

But Hagel told the service leaders Wednesday that he “also believes there must be more urgency behind these efforts” and that all Pentagon leaders must “put renewed emphasis on developing moral character and moral courage in our force.”

Kirby was asked whether Hagel believes ethics lapses are a symptom of over-use of the military for the long wars in Iraq and Afghanistan.

“He believes that that is a factor that should be looked at,” the spokesman said.

A significant portion of the concern about military misbehavior is aimed at two segments of the nuclear force: the Air Force’s land-based nuclear missile corps, and the Navy’s training program for operators of nuclear reactors used as propulsion systems for submarines and aircraft carriers. Neither of those fields was directly involved in significant ways in either of the wars since 2001.