Two senior House members yesterday asked the General Accounting Office to investigate whether administration officials misled Congress and should be prosecuted for withholding internal studies showing that the controversial Clinch River breeder reactor will cost $390 million more than publicly claimed.

Rep. John D. Dingell (D-Mich.), chairman of the Energy and Commerce Committee, and Rep. Richard L. Ottinger (D-N.Y.), chairman of its energy conservation and power subcommittee, accused the Energy Department of purposely withholding information that would have been "extremely damaging" to the decade-old nuclear project.

They asked the GAO to consider especially whether there are grounds for referring the case to the Justice Department for possible prosecution under statutes governing false official statements and obstruction of justice.

Their action comes as the Reagan administration prepares to seek a final government appropriation of $1.5 billion for the breeder, so called because it would "breed" more plutonium fuel than it consumes, in exchange for an additional private investment of $150 million.

Unless Congress approves the new appropriation, presumably as part of the omnibus continuing resolution for fiscal 1984 that it will take up later this month, federal spending on the partially completed nuclear project in Oak Ridge, Tenn., will cease on Sept. 30.

The question of the ultimate cost of Clinch River, which has more than quadrupled since it was launched a decade ago, has been of increasing concern to a Congress that has come closer with each passing year to killing the project.

Dingell's call for an investigation stems from discovery of a memo from the Energy Department's Independent Cost Estimating Group which concluded that Clinch River would cost more than $300 million more than the department was telling Congress on the eve of a vote last December.

The memo said the ICE staff "did not agree" with the $3.6 billion estimate that the department was giving Congress since its own estimate was $3.917 billion.

The ICE staff also said it felt that construction of the breeder would take 65 months rather than the 57.5 claimed by the Energy Department, "primarily because the installation rates assumed are 1.5 to 2 times the maximum ever achieved on a reactor plant."

However, the ICE staff said that "due to the major political problems and intervention problems on Clinch River , at the request of the assistant secretary for nuclear energy Shelby T. Brewer , we have held our ICE estimate close and have not published it."

Three days later, the Senate approved continued funding of Clinch River by a single vote.

Since then, the ICE staff has concluded that completion would take at least a 1 1/2 years longer than the 1989 date claimed by the Energy Department, with a likely cost escalation.

Dingell and Ottinger, in calling for an investigation, said the documents obtained "suggest that the assistant secretary misled Energy Secretary Donald P. Hodel who, in turn, felt he may have misled the president and the Congress."

Hodel, in a sharply worded memo to Brewer on Aug. 19, ordered him to prepare a new cost estimate that was "as fair and realistic as humanly possible" rather than one based on "speculation or idealistic hopes" so Congress could be confident that "we are dealing with this issue in good faith."