A General Accounting Office report released yesterday challenges some of the statistics that President Reagan used in his State of the Union message to prove his administration has reduced waste and fraud in government.

The GAO study, which was requested by Rep. John D. Dingell (D-Mich.), said some figures supplied by the President's Council on Integrity and Efficiency were inaccurate, misleading and, in one case, "scratch paper" estimates. But the council yesterday said it was sticking by its figures.

Reagan said the council had saved more than $2 billion during a six-month period in 1981 because of aggressive audits and investigations by federal inspectors general. His statements were based on two reports issued by the council, which was created in March, 1981, to coordinate the inspector general program.

The GAO criticized both reports. It said, for example, that the council had claimed the Transportation Department had "recovered" $190 million during one six-month period, yet, when the GAO investigated it found DOT officials didn't have any idea how much money the agency had "recovered." Instead, the GAO said, $51 million worth of expenses were being "questioned" by the agency and another $139 million were costs that the agency said it had avoided.

The GAO said that because of poor reporting, the council counted DOT's $139 million figure twice, which inflated its figures. It also said the council took credit for $538 million in Defense Department savings that really were made during the last year of the Carter administration.

Robin Raborn, spokesman for the council, said some methodology problems were caused because the council is so new. She said the council had found that $139 million at DOT was "unintentionally overlapped" in the report, and made that error public in January. The council counted some Defense Department savings, initiated during the Carter administration, she said, because the final audit of those items was done by the Reagan administration. The council has revised its figures, Raborn said, but it still believes it saved $1.9 billion during the six-month period, still close to the $2.1 billion figure that the president passed along.

While GAO didn't provide its own total figure, Dingell said the president's number should be cut by at least $1 billion.