President Reagan is expected to issue a directive soon that will require federal agencies to make their work places safer in hopes of lowering the skyrocketing cost of worker compensation.

The directive will require 15 large agencies to work closely with the Occupational Safety and Health Administration to reduce their injury rates by 3 percent for each of the next five years.

If that goal is met, OSHA said the government could save an estimated $7.8 million in fiscal 1984 and more in future years.

OSHA also plans to begin monitoring the progress of agencies more closely and may conduct "surprise inspections" at agencies with high accident rates.

Federal compensation claims jumped from $179 million in 1973 to $830 million in 1982, and are "rapidly approaching the $1 billion mark," according to OSHA Administrator Thorne G. Auchter.

Auchter said 98 percent of all injuries occured at the 15 agencies that will be targeted by the directive. The 15 are the U.S. Postal Service, General Services Administration, NASA, Tennessee Valley Authority, Veterans Administration and all the Cabinet departments except the Education, Energy and State departments. They do not necessarily have the worst accident rates in the government, but they produce most of the accidents.

In 1981, according to OSHA, the government averaged 3.03 "serious injuries" per 100 workers. Those were defined as any occupational injury or illness that caused a worker to miss a day of work. Eleven agencies exceeded the government average, with the Tennessee Valley Authority, Architect of the Capitol and Government Printing Office posting the worst accident rates.

Last month, Auchter asked the Cabinet Council on Management and Administration, which is chaired by presidential counselor Edwin Meese III, to approve the directive. A White House official said this week that it is "in the works."

Since 1970, federal agencies have been required to administer their own health and safety programs, with guidance from OSHA. But OSHA rarely paid attention to them, Auchter said, and, as a result of "several years of neglect," many agency plans are out of date or poorly administered.

OSHA wants to use a carrot-and-stick approach to make federal work places safer, said Thomas McCully, a special assistant at OSHA who monitors federal health and safety. While the agency is prohibited from assessing fines against federal agencies, McCully said, it can conduct surprise inspections and send its findings to the presidential council.

An official who takes steps to lower an agency's accident rate could qualify for a presidential award, he said. The Office of Personnel Management now has agreed to include safety and health matters in performance ratings of federal managers.

OSHA also has doubled the number of federal employes it trains and is improving its injury information system, Auchter said. Currently, federal agencies report deaths, injuries and serious illnesses to OSHA through the Federal Accident Reporting System, but Auchter says that system is "clumsy and duplicative." He wants to rely on worker compensation claims, which, he contends, are more accurate and detailed.

Since expanding its efforts, OSHA has evaluated health and safety programs in the Navy, Postal Service, VA and TVA, and currently is studying the Justice Department.

All of those agencies have taken steps to improve, but the changes will not be permanent unless top management makes accident prevention a priority, Auchter said.

There are two agencies with high injury rates that OSHA won't be able to touch, however. The Architect of the Capitol's Office and Government Printing Office are part of the legislative branch, which Congress exempted from coverage under the federal occupational safety and health standards.