Secretary of Health, Education and Welfare Joseph A. Califano Jr. said yesterday that taxpayers are losing $1 million a year through government payments of ineligible Medicaid claims.

Appearing on "Issues and Answers" (ABC, WJLA). Califano said a recently completed review of outlays from April to September, 1976, indicates that 4.7 million Medicaid claims totalling $229 million were paid improperly.

When the figure is projected on an annual basis and state matching funds are counted, "just in terms of ineligible payments, we're throwing $1 billion a year away in this country," said Califano.

An HEW aide emphasized that the ineligibility applies to health care providers as well as to the low-income recipients of the health care program.

Califano cited the figures in denying published reports that the Carter administration is abandoning its so called "Project Intergrity" to root out abuses in the program, which cost about $15 billion in 1976.

He said HEW has screened about 250 million transactions and turned up 47,000 involving doctors and druggists "which appear to us to be improper or questionable," although not all neccessarily involve fraud.

Of these cases, 2,5000 are being investigated on a state-by-state basis for criminal prosecution or civil action, Califano said, and as these are processed, more cases will be submitted for action." . . . We have come into a system that has grown like topsy, that inadequate attention has been paid to over the past several years," Califano said, "and we move as fast as we can."

On other issues. Califano joined Secretary of State Cyrus R. Vance (on NBC's "Meet the Press") and Energy Secretary James R. Schlesinger Jr. (on CBS' "Face the Nation") in denying that administration initiatives are foundering.

Califano predicted that legislation will be enacted this year to make Social Security "viable," that hospital cost containment "can be enacted if Congress stays in session long enough," and that subcommittee action on the administration's welfare package will be completed by Christmas. "I think we are doing better than we are getting credit for," he said.

Similarly, Schlesinger expressed optimism that the administration's Senate-ravaged energy program will come out all right in the end. Likening its congressional progress to the "perils of Pauline," he said the energy program survived predictions of doom in the House and "I would not be surprised if we went through the same cycle with regard to the Congress as a whole."

Echoing President Carter's criticism of the oil companies for opposing the programs, Schlesinger said the "general tenor of the oil industry is wholly unsatisfactory," but he rejected holding a threat of divestiture "as a clun" over the industry's head.

On foreign policy, Vance rejected charges that the administration is trying to do too much too fast and pushing for a Geneva conference on the Middle East in order to score a diplomatic success before the end of the year.

He said Carter was confronted at the start of his administration with critical Middle East, arms control and southern Africa problems, among others, and "although it would be nice to deal with fewer problems, we simply had to go forward and seize these problems."

Asked if President Carter is adding Saudi Arabia to his eight-nation world trip next month. Vance deferred answering. Newsweek magazine reported yesterday that Carter was expected to approve a stopover in the oil-rich nation to dramatize the importance of his energy program.