Federal officials have opened the first national investigation into alleged kickbacks and price-fixing in the Summer Food Service Program for needy children.

Justice and Agriculture Department investigators have found evidence that the government may have been defrauded of millions of dollars by private food management companies that provide the free lunches through more than 2,000 religious and other charitable organizations.

The $160 million program paid for lunches for 3.7 million children from low-income areas last summer.

The Arigulture Department has assigned nearly 25 agents to the investigation, which is taking place in at least five cities - New York, Chicago, Philadelphia, Newark, N.J., and Miami.

Assistant U.S. attorneys from the five cities met here three weeks ago to be briefed on the Agriculture Department investigation by investigation coordinator Patrick Clerkin.

Clerkin, according to well'placed sources, outlined alleged fraud in the summer feeding program which included theft of food, substandard food, kickbacks, price-fixing, adult use of food intended for children and the dumping of extra food for which the government had paid.

An official described the same as one of the "ugliest" he had seen in which food service operators who had successfully defrauded the program in one city have expanded to others.

In New York City, food management companies charged the federal government for feeding 52,000 children a day while 26,000 children were reported eligible in the area served, according to information presented at the Agriculture Department briefing.

The religious and other charitable organizations are not the main targets of the investigations, but the FBI is investigating allegations that in some cases the food suppliers agreed to kick back a portion of the overcharges to the sponsoring group in order to obtain the child-feeding contracts.

In one case, a food service company in Philadelphia agreed to pay $1,500 for tickets to a religious dinner sponsored by the group which provides the lunches, according to FBI dociments obtained by The Washington Post.

Investigators are studying previous local convictions to learn the potential variety of fraud elsewhere. In one Atlanta case, according to other FBI documents, children were regularly served only a quarter glass of milk but were given a full glass on the days federal inspectors were expected.

In another case in Dublin, Ga., a preacher used his church as a day-care center, charged the government $16,384 for feeding children in June, 1970, but spent only $3,662 for their meals. He fabricated invoices to get reimbursed.

In South Carolina, a pastor collected $6,986 to cover costs of $1,767, with most of the money spent on lunches for ineligible children. And in New York City, the administrators of a food program funded no-snow jobs for other employees.

Robert E. Magee, deputy director of Agriculture Department investigations, confirmed last week that the probe was under way.

"We are now and have been investigating the summer feeding program in coordination with appropriate U.S. attorneys," he said.

The case has not yet reached grand jury action, according to an official close to the investigation, but is expected to this spring.

The potential for fraud is also great because only 12 per cent of summer feeding sites are schools, whose programs are under stricter control, whereas nearly all the federally subsidized lunches served by the Agriculture Department during the regular school year are distributed in school cafeterais.

Legislation authorizing the program exprises next fall, and no funds had been included in the Ford administration's proposed 1978 budget. But the Carter administration has restored USDA's 1978 budget request of $230 million.

The summer fedding program is administered by the Food and Nutrition Service of USDA. In two years, the number of participating religious and charitable organizations has doubled.

The program was first funded in 1969 under the Child Nutrition Act, and average daily participation of children has grown from 2 million in 1974 to the 3.7 million last year.