The Reagan administration will publish final regulations today barring illegal aliens from public housing and other housing assistance and requiring the eviction of those already receiving aid, according to a Department of Housing and Urban Development spokesman.

More than 10 million people now living in public housing or receiving rent supplements or mortgage interest assistance would be affected by the rules, a HUD official said. All will have to prove that they are U.S. citizens or legal alien residents of this country in order to continue getting housing aid. The same proof will be required of prospective recipients of housing aid.

The restrictions are being imposed in an effort to "reserve scarce housing assistance resources" for U.S. citizens and other legal residents "with the most legitimate claim," according to a HUD statement.

Barring illegal aliens from housing aid has been controversial in the five years since legislation requiring the action was passed, because "a lot of people think those folks need housing, too," said Roberta Youmans of the National Housing Law Project. Some opponents fear that discrimination against Spanish-speaking Americans could result.

HUD Secretary Samuel R. Pierce Jr. defended the regulations, saying: "I feel sorry for American citizens who are poor and who need the space [illegal residents] are taking up in our housing."

The government "shouldn't house illegal aliens," he added. "They sneak into our country. They must realize when they do this that they are putting their own safety, health and future in jeopardy."

Pierce said that the agency does not know how many illegal aliens are receiving housing assistance, but that other agency officials, as well as some advocacy groups, believe the number is substantial.

Legislation barring illegal aliens from housing aid was approved in 1981. HUD published regulations, but never put them into effect. Then, in 1983, Congress deferred implementation of the law until November 1984.

The delay was voted because Congress, HUD, subsidized housing project owners and others "recognized" that enforcement of the law would "produce extraordinary hardships, excessive paperwork and unnecessary financial difficulties for the individuals, the owners and, in some cases, the federal government," Youmans said in testimony before a House subcommittee last year.

She predicted that thousands of families would be evicted from subsidized housing, including U.S. citizens or aliens living in this country legally "because other members of their household cannot meet the documentation requirements." Other citizens and legally resident aliens would be denied housing for the same reason, she said.

Under the regulations, occupants of public or subsidized housing will be given at least 75 days to produce evidence of citizenship or legal residence for all members of the household 18 and over, according to Steven L. Balis, legal adviser in the HUD general counsel's office.

Landlords in subsidized housing will continue to receive their subsidies during the period needed to evict an ineligible tenant, with the length of time varying, he said. Local HUD offices will establish the time limit, based on local conditons.

Legislation that would reverse the law denying housing aid to illegal aliens has been proposed but has not been successful, a congressional aide said.

"It's a complicated problem, particularly for Spanish-speaking Americans," she said, noting that if documentation required to prove citizenship or legal residence status is difficult, "landlords might not want to rent to any Spanish-speaking people, which would increase discrimination against them."

The regulations will take effect July 30, giving HUD time to distribute instructions and forms to public housing agencies and owners of subsidized housing. After that date, applicants will have to document their U.S. citizenship with birth certificates, passports, naturalization or baptismal certificates, or Bureau of Indian Affairs documentation of tribe membership. If none of these documents can be found, HUD will accept a statement from another person who knows the applicant and is willing to verify the citizenship.

Resident aliens can use their alien registration receipt cards (the so-called "green cards"), or other documents issued by the Immigration and Naturalization Service, and must produce current documents proving their status each year that they receive housing aid.

Families now in public housing or getting other assistance will have to document their citizenship or legal residence the first time after Oct. 27 that the annual review of their income takes place. The regulations require legal resident aliens receiving aid to prove that they are eligible each year. Citizens will have to provide proof only once.

Public housing officials or subsidized project owners will be authorized to give current residents extensions of up to 90 days to get their documents in order.

In a release describing the new rules, HUD notes that "similar restrictions already are in effect for recipients of other Federal low-income assistance, such as food stamps." Applicants for food stamps can be asked to prove legal residence or citizenship, but the program has no uniform requirement for such proof.

Occupants of about 4.16 million housing units are covered by the new regulations, according to Balis. Residents of about 2.1 million of the units get Section 8 rent subsidies, which pay the difference between 30 percent of family income and the fair market rent for the area as established by HUD, or receive assistance through vouchers provided by a similar rental aid program.

Other recipients are in a program that provides mortgage interest subsidies for owners of projects, and still others come under a plan that subsidizes mortgage interest for low- and moderate-income homeowners. To obtain interest subsidies, buyers will need proof of citizenship or legal residency status to qualify for home loans, Balis said.