As millions of homeless people faced freezing temperatures this week, critics charged that federal foot-dragging is holding up funds that are badly needed for shelters and other aid.

A congressional report criticized the Department of Housing and Urban Development, which decides who will get funds, for withholding money from religious organizations that aid the homeless. Throughout the nation, people are helped in shelters operated by churches and other religious institutions, according to the report issued by the House Government Operations Committee.

An estimated 2 million to 3 million Americans are homeless, more than at any time since the Great Depression, according to the National Coalition for the Homeless. Families with children account for one-third to one-half of all homeless people, the coalition said.

In its own report last week, the coalition said some federal agencies, particularly HUD, have waited for months before implementing laws. In the case of $15 million appropriated to aid elderly people and families with children, the department did not move to distribute funds until after the coalition filed a lawsuit, the report said. "At the same time," the report continued, "congressional failure to provide full 1988 funding threatens the future and stability of the programs."

When the lawsuit was filed, HUD Undersecretary Carl D. Covitz said the agency had delayed distributing funds because it wanted to help local groups find "creative" ways to use the money rather than merely hand it out.

Congress appropriated $15 million to pay for two new programs for the homeless in 1987. An additional $1 billion in 1987 and 1988 was authorized under the Stewart B. McKinney Homeless Assistance Act, passed last spring, and Congress appropriated $355 million of the amount for fiscal 1987, which ended Sept. 30. But so far, "only a fraction" of the $616 million authorized for fiscal 1988, which started Oct. 1, has been approved, according to the coalition.

HUD has refused to give any money directly to churches or predominantly religious organizations, citing constitutional requirements for separation of church and state. Critics in Congress and in organizations maintaining shelters for the growing homeless population said religious groups historically have cared for the destitute and should receive federal assistance.

In proposed regulations governing use of emergency shelter grants for renovating or converting buildings, HUD had said churches and religious organizations that want to apply for funds must first establish separate companies or other legal entities to which they can transfer ownership of property to be used as shelters.

By the time the final regulations were published in October, the department had modified the requirements to allow churches to lease property to the separate entities and then enter into contracts allowing the churches to operate the facilities. The agency made the change because officials have been "particularly struck by the vital and unique role" religious organizations play in aiding those in need of shelter, according to HUD comments published with the regulations.

But the House committee report said the solution of establishing separate legal entities "is neither constitutionally required nor very practical with respect to emergency shelter grants." Amounts needed to rehabilitate structures often are relatively small, $10,000 to $20,000, making it "economically inefficient" for a religious organization to set up separate legal entities, the report said.

In the past, the report said, there have been "many instances {in which} it has been possible for HUD and other agencies to delineate acceptable rules that do not breach the barrier between church and state." While recent regulations prohibit the use of federal funds to rehabilitate or convert church-owned buildings, other HUD rules say religious organizations can be allocated federal funds to cover operating and social service expenses of homeless programs.

"It boggles the mind that with another cold winter upon us and hundreds of thousands of homeless desperately seeking shelter, HUD is going out of its way to deny funds to religious groups to shelter the homeless," Rep. Tom Lantos (D-Calif.), chairman of the committee's employment and housing subcommittee, said in a statement issued with the report. Lantos called the Reagan administration "hypocritical in the extreme" in the stance against aid to church-owned shelters while at the same time it is "bent on putting prayer in the classroom and subsidizing religious schools ... . "

The committee report recommended that HUD revise its regulations to make grants available to religious groups without "compromising the constitutional mandate of separation of church and state." The test for a group's eligibility to receive federal funds "should not be whether the facility is owned by a religious organization or ... by a separate legal entity set up by that organization," but whether sheltering the homeless "can be segregated or separated out from the sectarian activities of the religious organization ... . "

HUD officials declined to comment on the committee report because they have not seen it, a spokesman said.

In its report, the coalition for the homeless said HUD programs authorized by Congress "have operated unevenly," with funds often being "distributed ... with extraordinary delay." Most of the money appropriated under the 1986 legislation, however, "has now reached the streets and is making a difference in the lives of homeless Americans," the report said.

But the coalition said the Department of Education "has failed to implement its programs to aid homeless children," which was authorized in the McKinney legislation, and the General Services Administration "has taken no action to make surplus government property available for the homeless," also required by the measure.

It takes federal agencies from six months to a year to write regulations for a new program and put them into effect, the HUD spokesman said. "I do believe everybody here has been working as hard as we can to get this money out," he said.