Gates issued a memo Tuesday after reflecting on results of the independent review he directed after the incident to ensure the safety and health of servicemembers, civilian defense employees, and their families.

‘‘I ask all commanders, supervisors, noncommissioned leaders and other personnel in the department to reinforce the fabric of trust with one another,” Gates wrote. ‘‘From simple everyday expressions of concern, to supervising, mentoring and counseling, we, and every servicemember, need to be more attuned to one another’s mental, emotional and spiritual balance and be willing to take responsible action.”

Gates urged department members to look beyond their day-to-day tasks and challenges and take action if their colleagues appear to be at risk.

He also called for leaders to be honest in their assessments of their subordinates — particularly when they identify red flags — and to document what they identify.

Maj. Nidal Malik Hasan, an Army psychiatrist, is charged with killing 13 people, 12 military and one civilian, and wounding 43 others during a Nov. 5 shooting rampage at Fort Hood.

Hasan, a Muslim, allegedly became radicalized and complained to colleagues about his role as a U.S. military officer when he was posted at Walter Reed Army Medical Center before being assigned to Fort Hood in July.