Last year a new federal-state program aimed at "runaway fathers" helped the states collect $1.5 billion in child support by tracking down absent parents of low-income and welfare children, according to a report published yesterday by the Department of Health and Human Services.

Total administrative costs for the program last year were $450 million, about one-third of what was collected.

Using sophisticated new blood-testing techniques, the states established the paternity of 144,467 children. In many other cases, the paternity of the father was already known but he had fled and was no longer helping the mother support the child. All told, collections were made under the program from parents of nearly 900,000 children at the rate of roughly $1,800 per child for the year.

Louis Hays, deputy director of the Office of Child Support Enforcement, said that the blood tests being used to help establish paternity were first developed by the medical profession for an entirely diffent purpose, as a way of matching organs from donors with persons needing transplants. In these cases, Hays said, precise matching is required.

"The blood tests have become so sophisticated" and tell so much about genetic makeup that when used in paternity cases there is a "99 percent certainty," Hays said . But he said the tests are only one form of evidence that the courts consider in paternity cases. In 1976 the program helped establish paternity in only 14,000 cases, but the figure has grown steadily to the current 144,467 number for 1980.

Six years ago when Sen. Russell B. Long (D-La.) first pushed through the legislation providing the federal financing for the program, also called the "fleeing fathers" or "nab-a-dad" program, lots of welfare experts said it would be fruitless. They said the fathers involved were generally so poor that it would be hard to extract any money from them.

Others said some of the welfare mothers would be put in jeopardy of physical violence from men traced with their aid and forced to pay.

Since then the program has been collecting more and more money and vocal opposition has died down.

Under the program, the federal government pays 75 percent of administrative costs for state and local child support offices. The idea is to reduce government welfare costs by making the absent parent meet his support obligation. Whenever a woman comes into a state welfare office to ask for aid under a program of Aid to Families with Dependent Children, she is asked to help identify and locate the father.

Most of the absent parents live in the same community or state as the mother, and usually the state offices can find them by checking state auto registration files, state tax records, unemployment insurance records and sometimes just telephone books.

But sometimes the state can't find the father and then it can use the federal locator service and the Internal Revenue Service. From Social Security, the IRS and federal employe records, it can get the address of the parent being sought; and under a separate statute, it can also get from the IRS information based on tax returns about the absent parent's income and assets. The IRS can later be enlisted to help collect money owed, and a new proposal even permits taking it out of tax refunds due.

The Reagan administration has before Congress several proposals to strengthen enforcement powers further.

Since the start of the program in fiscal 1976, collections have totaled $5.4 billion, and costs about $1.6 billion. In 1980 total collections in the District of Columbia were $1.6 million with 737 paternities established, in Maryland $26.4 million with 8,330 paternities established and in Virginia $8.8 million with 1,712 paternities established