Inspectors general at federal agencies saved the government $5.7 billion during the six months that ended Sept. 30, the chairman of the President's Council on Integrity and Efficiency said yesterday.

Joseph R. Wright Jr., deputy director of the Office of Management and Budget, said the IGs have saved the government a total of $16.9 billion over the past 20 months.

The administration's effort to "follow every lead, root out every incompetent and prosecute any crook who's cheating the American people" is working, Wright said.

This was the second time this year that the administration has held a White House news conference to announce the savings achieved by the IGs. Congressional committees and the General Accounting Office have criticized past reports, saying, among other things, that they are "padded" because they consider "costs avoided" as direct savings.

But Wright defended the administration's reporting practices yesterday, and cited several examples.

He said Defense Department auditors renegotiated a $1 billion, two-year contract for aircraft engines, cutting the price by $96.4 million. Another $1.8 million was saved at the Commerce Department because IGs denied a number of risky loan and grant applications that Wright asserted probably would have been accepted in the past.

Overall, Wright said, $9.9 billion had been saved since April, 1981, through defense contract audits, $4.9 billion in costs that had been avoided and $2.1 billion in overpayments that had been recouped or fines collected.

Wright cited the increased use of computer matching as a major money-saver. So far, he said, computer matching has identified more than $24 million in overpayments to persons who had underreported their incomes. Officials currently are developing a national computerized file of deceased beneficiaries to prevent payments to those who have died.

Because the IGs' accomplishments have not received as much attention as the administration would like, OMB considered, but quickly rejected, the suggestion that it adopt a dog from a local humane shelter as its mascot and offer photographers the opportunity of photographing Reagan with the "watchdog."

Instead, the White House sent presidential counselor Edwin Meese III, who joked, when he was asked if he were the "junkyard dog," "No, I'm the bones."