The federal government collected more than $1 billion in child support payments from fleeing fathers in fiscal 1978, the Department of Health, Education and Welfare said yesterday.

The program was set up to track down fathers who have avoided child support and make them pay. In fiscal 1978, $1,050,633,099 was collected by HEW and local agencies under the program at a total administrative cost of $320 million, HEW reported.

The program was set up under legislation sponsored by Senate Finance Committee Chairman Russell B. Long (D-La.) in 1975.

Program services are available both to parents of children on welfare and to nonwelfare families that seek state help in finding absent parents and enforcing financial responsibility.

HEW Secretary Joseph A. Califano Jr. said state and local governments saved $187 million in welfare costs last year because of the program, and 29 states reported they were able to take 19,000 families off the welfare rolls.

The program operates through an elaborate system of information exchanges, under which local governments can seek HEW aid in locating a father through job and tax records, establishing paternity through blood tests and other methods, and getting legal orders to make the parent pay.

Since the program began in August 1975, $2.6 billion in support payments has been collected at a cost of $787 million, but fiscal 1978 was the first year in which collections reached $1 billion.

The HEW report shows that collections for the District of Columbia totaled $777,083 in fiscal 1978.For Maryland the figure was $12.3 million, and for Virginia $4.6 million.

The leading states in collections were Michigan, $212 million; Pennsylvania, $165 million, and California, $148 million.

When the program was first proposed by Long, some welfare experts scoffed at the concept, arguing that the fathers in question had little money to pay child support, therefore collections would be low. But program officers have found that in many cases the absent father of a welfare child has a substantial income.

Where the state is seeking a payment on behalf of a welfare mother, she is required to cooperate in helping identify the father and locate him, or face possible loss of welfare benefits.