President Carter took is anti-inflation message to a gathering of state and local welfare officials yesterday, telling them that in a time of budget austerity rooting out waste and fraud in their programs is the best way to show compassion for the poor.

"When a program is poorly managed-when it is riddled with waste and fraud-the victims are not abstractions, but flesh-and-blood human beings," the president told about 1,000 persons at a Department of Health, Education and Welfare conference at the Washington Hilton Hotel.

"They are the unemployed teenagers who get shut out of a job; they are the senior citizen deprived of a needed medical service; they are the school child who goes without a nutritious meal, or they are taxpayers whose hard-earned dollar goes down the drain."

Elimination of "fraud and waste" from domestic programs is expected to be a major theme of the Carter administration next year He speech yesterday is also part of the Hite House response to liberal critics who are already complaining about proposed budget cuts next year in social welfare programs.

"Those of us who believed that our society has no obligation toward its weakest members have the greatest stake in improving the management and efficiency of the programs that are designed to meet the obligation," the president said. "This is especially true when the battle against inflation makes it impossible to bring vast new resources to bear on our social problems.

"There is no room any longer for waste," he continued. "At such a time-indeed, at any time-efficient management is in itself an act of compassion, for it unlocks new resources to be used for human ends."

Carter described as a "myth" the idea that "it is somehow more compassionate, more committed, to appropriate another billion dollars of the tax-payers' money than to streamline an existing program so that it delivers an extra billion dollars worth of service."

In fact, the president added, the opposite is true: "Efficient management increases political support for a program among those whose taxes pay for it. It gives the lie to those who prefer to believe that programs that meet human needs cannot work. It inspires and boosts the morale of government employes who are deeply frustrated when their hard work is frittered away through waste and fraud."

Such arguments are likely to be heard repeatedly from the White House in the coming months as the president seeks to reconcile his budget-cutting measures with the pressure from other Democrats to spare domestic welfare programs.

Carter told the conference that he has directed budget director James McIntyre and HEW Secretary Joseph A. Califano Jr. to head an effort to steamline federal eligibility requirements for public assistance programs. A task force in the Office of Management and Budget is already at work on the project.

He also said he intends to extend the recently enacted inspectors general program throughout the government-ordering every agency and department to produce its own plan to eliminate waste and fraud in its operation.

In HEW, Carter said, Califano has already pledged to save $1 billion during the current fiscal year by eliminating waste and fraud.

The president also asserted that continued government reorganization projects are "a top priority" for him. White House aides have been divided over how much importance to place on the reorganization effort next year, when the anti-inflation program and a predicted debate over a new arms agreement with the Soviet Union are expected to take up a major share of the adminstration time.

Carter told the state and local officials, who listened to him in silence and applauded politely at the end, that he does not believe Americans are prepared to turn their backs on the needy.

"The American people will not accept callousness toward those among us who are aged or sick or jobless or lacking in education or opportunity," he said. "But neither will the American people accept a massive bureaucracy that is too clumsy or too poorly managed to do the job." CAPTION: Picture, Califano introduces president to HEW conference on waste and fraud in government. By Frank Johnston-The Washington Post