President Reagan urged his inspectors general yesterday to "keep on being as mean as junkyard dogs to protect the taxpayer" after they told him they have saved $2 billion in six months by curbing waste and fraud in government.

The president appeared unexpectedly in the White House press room to praise his IGs in response to their report claiming that, in the six months ending Sept. 30, indictments in federal waste and fraud investigations were up 59.5 percent over the previous six months, convictions were up 28.1 percent and phoned-in tips of possible wrongdoing were up 80 percent. During that period, there were 657 convictions and 1,179 indictments of federal officials or people accused of defrauding the government.

"I promised we'd follow every lead, root out every incompetent and prosecute every crook that we found cheating the people of this nation," Reagan said. "This pledge has been and will continue to be kept."

The $2 billion in claimed savings includes $405 million actually recovered by the government and another $1.7 billion in costs avoided during the six-month period, according to Edwin L. Harper, deputy director of the Office of Management and Budget and chairman of the President's Council on Integrity and Efficiency.

The report was a government-wide compilation of statistics, many of which had previously been reported separately. It is clear, however, that the Reagan administration is putting a higher priority on uncovering federal wrongdoing than its immediate predecessors.

The IGs have had to accept few budget and personnel cuts while their departments are being trimmed; they are encouraged to seek publicity for their accomplishments, a top-level OMB manager has been assigned to monitor and enourage their efforts and yesterday marked the second time the president has publicly led cheers for them. Some of the highlights of the report and yesterday's press conference:

* The Defense Department is organizing a task force of 100 investigators to watch over defense procurement practices. The task force will save taxpayers between $500 million and $1 billion annually, according to Joseph H. Sherick, assistant to the secretary of defense and the department's IG.

* A total of 145 federal employes have been fired nationwide as a result of IG investigations in the past six months. Thirty-four of those employes were from DOD, and 18 of those DOD employes were snared in a "sting" operation at a supply depot in Memphis. Sherick said that his task force will specialize in undercover work.

* Computer list matching techniques have been used to find double-dippers in the entitlement programs. Richard P. Kusserow, inspector general of the Health and Human Services Department, described HHS's efforts on such things as "death-termination interface"--or discovering that millions of dollars worth of Social Security checks were being sent to dead people by cross-checking a list of deceased Medicaid recipients with Social Security lists.

* Departments and agencies are committed to collecting $1.5 billion a year in debts that are due the government, and the IGs are coordinating that effort. It is estimated that the government pays $10 million daily in interest on its $25 billion in delinquent debts.

When Reagan met privately with the IGs yesterday, he told them, "You certainly have brightened my day. I was thinking of having an executive order to outlaw Monday morning."