The warning follows an analysis by the FBI and the Homeland Security Department of the siege that killed nearly 340 people, many of them students, in the city of Beslan last month.
The safety advice is based on lessons learned from the Russia incident.
Federal law enforcement officials also have encouraged local police to stay in contact with school officials and have encouraged reporting of suspicious activities, the letter says.
In particular, schools were told to watch for activities that may be legitimate on their own but may suggest a heightened terrorist threat if many of them occur.
Among those activities:
• Interest in obtaining site plans for schools, bus routes and attendance lists;
• Prolonged "static surveillance" by people disguised as panhandlers, shoe shiners, newspaper or flower vendors or street sweepers not previously seen in the area;
• Observations of security drills;
• People staring at or quickly looking away from employees or vehicles as they enter or leave parking areas;
• Foot surveillance of campuses involving individuals working together.
The effort is the latest by the Education Department and other federal agencies to encourage school officials to maintain and practice a plan for responding to emergencies.
The federal government is advising schools to take many steps to improve the security of their buildings. Those include installing locks for all doors and windows, having a single entry point into buildings and ensuring they can reach school bus drivers in an emergency.
