Prospects for a near-record federal pay raise brightened yesterday when the president's own pay "agents" announced that an average increase of 13.5 percent would be needed this October to bring U.S. white collar salaries up to industry pay levels.

The biggest U.S. pay increase in recent times was a 16 percent raise in 1945. The largest increase since the government began linking its wages to industry was a 9.1 percent raise almost 10 years ago.

More than 300,000 civil servants in the Washington area stand to benefit from the U.S. pay increase that comes due this fall. President Carter has not set the final amount yet. Last year the president had budgeted only 5.5 percent for them.

The recommendations by the pay agents -- the secretary of labor and the directors of the Office of Management and Budget and the Office of Personnel Management -- will be formally sent to Carter early next month. By Aug. 31, he will have a pay proposal plan ready to send Congress. m

Aides to the president said he has not seen the agents' recommendations, and has not decided on what amount he will set for the October 1980 U.S. pay raise.

Under the complicated "Comparability Pay Act" that governs white collar federal pay-setting, U.S. workers are supposed to get annual pay raises that will keep them even with pay for similar jobs in the private sector.

The Bureau of Labor Statistics makes an annual pay survey of selected industries (excluding state and local government employes), and reports to the president's pay agents.

They in turn use that data to come up with recommendations for the president.

The BLS survey -- for the period March 1979 to March 1980 -- showed that private industry pay had gone up an average of 9.1 percent. Using that data, and also taking into account raises denied federal workers in past years, the pay agents say it would take an average 13.5 percent this October to even out U.S. pay scales to industry levels.

Hours before the pay agents' report was issued, the president of the government's largest union predicted that Carter would okay an October raise of 9.1 percent. Kenneth T. Blaylock of the American Federation of Government Employees said the figure would be "politically" feasible. This is a year in which the president is caught between an angry, resentful work force that feels it has been pummeled unfairly by the White House, and a conservative opponent, Ronald Reagan, who has not put big federal pay raises high on his list of promises.

The complexity of the pay situation is compounded by the fact that there are at least four pay figures kicking about.

Carter proposed a 6.2 percent raise in his budget this January, then upped that figure to 7.8 percent in the mid-budget review released last week. The BLS data shows a March-to-March industry pay gain of 9.1 percent. Now the pay agents have said 13.5 percent is needed to maintain "comparability."

Take your pick. The pay raise could be any of those four figures, or another one arrived at by the president. Carter aides say the final amount will depend in large part on weighing the political consequences that always haunt federal pay decisions in election years.

By law the "comparabiilty" pay raise figure goes into effect automatically in October unless the president proposes an alternative (lower) amount. If Congress rejects the "alternative plan" within 30 days then the higher "comparability" figure becomes the pay raise. If it okays the alternate plan, it becomes law in October.

The amount of the pay raise is still up in the air. It will be late August before the president decides what it should be. Whatever figure he picks, Congress is virtually certain to approve. But for federal workers who had hoped for 7.8 percent and anticipated a 6.2 percent raise, things are suddenly looking much, much brighter.