A General Accounting Office study that criticized President Reagan's plan to abolish the Energy Department has sparked a heated exchange between the Office of Management and Budget and Comptroller General Charles A. Bowsher.

The four-month study by Bowsher's GAO, released Aug, 2, concluded that the administration could not back up its claim that abolishing DOE would save more than $400 million a year. It also said the administration had not considered the cost of shifting most of DOE's functions to the Commerce Department and had not figured out how to accomplish such a major reorganization efficiently.

That outraged OMB Deputy Director Joseph R. Wright, who fired off angry letters to Congress the day after its watchdog agency's report was released. Wright characterized the GAO's report as "seriously flawed" and "misleading." Wright complained that the GAO never tried to interview him or key members of his staff, that it relied on out-of-date figures and that it focused on incidental benefits rather than the big energy picture.

Wright's letters, in turn angered Bowsher, who sent a 17-page reply to him and Congress. He said Wright's office had been contacted at noon June 1, but had deferred GAO's request for an interview to a Commerce official. Bowsher said Wright did not "accurately reflect the facts contained in the report or the evidence upon which the facts are based."

The administration submitted its legislation to abolish DOE two months ago, but so far it has been greeted generally with hostility and skepticism. The GAO report was expected to dash any lingering hopes that DOE could be abolished this session.