WASHINGTON — The Obama administration is moving forward with a plan to better track killings by police officers, as heightened national scrutiny of such deaths has reinforced criticism of its reliance on self-reporting by state and local law enforcement agencies.

In a notice published in the Federal Register this week, the Justice Department said it would ask law enforcement agencies and medical examiner’s offices to fill out forms when there is a news report or another indication that a person died while in police custody.

Under the proposed system, which would cover 19,450 state and local law enforcement agencies and about 685 medical examiner’s or coroner’s offices, they would also be asked to fill out forms about the total number of such cases every three months. The department’s Bureau of Justice Statistics would then compile that information.

The proposal comes as police killings of African-Americans have fueled protests in recent years in places like Ferguson, Mo., and Baltimore, and led to the rise of the Black Lives Matter movement. The resulting scrutiny of the issue has focused attention on the lack of reliable and comprehensive data about how many people are killed by the police each year.