LOS ANGELES  A growing number of big-city police departments and other law enforcement agencies across the country are embracing a new system to report suspicious activities that officials say could uncover terrorism plots but that civil liberties groups contend might violate individual rights.

Here and in nearly a dozen other cities, including Boston, Chicago and Miami, officers are filling out terror tip sheets if they run across activities in their routines that seem out of place, like someone buying police or firefighter uniforms, taking pictures of a power plant or espousing extremist views.

Ultimately, state and federal officials intend to have a nationwide reporting system in place by 2014, using a standardized system of codes for suspicious behaviors. It is the most ambitious effort since the Sept. 11 attacks to put in place a network of databases to comb for clues that might foretell acts of terrorism.

But the American Civil Liberties Union and other rights groups warn that the program pioneered by the Los Angeles Police Department raises serious privacy and civil liberties concerns.