President Carter asked Congress yesterday to grant permanent resident alien status to millions of illegal aliens in the United States, a first step that in five years could lead to American citizenship for people now living under the threat of deportation.

Unveiling a complex package of measures to deal with one of the most difficult domestic issues his administration has faced, the President said that the flood of illegal aliens "is severe and is getting worse."

To stem that tide, he proposed a series of steps including beefed-up border security, particularly along the border with Mexico, possible increased economic assistance to countries that are the major sources of illegal aliens and the imposition of civil penalties against employers who hire workers who entered the country illegally.

To deal with the millions of illegal aliens already here. Carter proposed to separate them into three categories:

Illegal aliens who entered the United States before Jan. 1, 1970, would be granted permanent resident alien status if they applied for it and provided proof of continuous residence in the United States since their entry. By law, they could apply for citizenship five years after receiving permanent reident alien status.

Illegal aliens who entered the country on or before Jan. 1, 1977. would be eligible to apply for temporary alien status for five years. What would happen to them after the five years is not settled and will depend in part administration officials said on what the registration process shows about their numbers, location in the United States and economic status.

Aliens who entered the country illegally since Jan. 1, 1977, would remain subject to deportation if apprehended.

Attorney General Griffin B. Bell insisted that the granting of permanent resident alien status to illegal aliens who have been in the United States for seven years or more did not amount to "amnesty." But under questioning, he called the plan "something like amnesty" and "far more than amnesty."

The President, Bell, Labor Secretary Ray Marshall and Leonel J. Castillo, the head of the Immigration and Naturalization Service, appeared in the White House press briefing room to announce the proposals.

Oficials said there are no accurate estimates of the number of illegal aliens in the United States. Bell said he has seen estimates ranging from 6 million to 12 million. One of the purposes of the new classification system, encouraging illegal aliens to register with the INS. is to obtain accurate information on their numbers, the officials said.

Under the proposal, illegal aliens would have up to one year after enactment of the legislation to apply for permanent or temporary resident status. Those granted temporary statuse for five years, unlike permanent resident aliens, would be ineligible for federal social services such as food stamps and Medicaid.

In his message to Congress, the President said he decided that granting "an adjustment of status" to longtime illegal aliens "is necessary to avoid having a permanent 'underclass' of millions of persons who have not been and cannot practicably be deported and who would continue living her in perpetual fear of immigration authorities, the local police, employers and neighbors."

Arguing that the main reason aliens enter the country illegally is to obtain a job. Carter asked Congress to enact a law that would impose on employers up to a $1,000 civil fine for each illegal alien they hired. But he said the Justice Department would act only against employers who engage in a "pattern or practice" of hiring illegal aliens.

The plan also directs Bell to designate what documentation of legal residence an alien must have to apply for a job. One of these will be a Social Security card, the President said, which the government will seek to restrict only to legal residents by requiring personal interviews of card applicants and by making the cards more difficult to forge.

Carter and Bell insisted that despite these steps, no effort would be made to make the Social Security card or any other document a form of national identification.

In other parts of the message the President proposed.

Imposing criminal penalties against persons who accept payment for helping illegal obtain jobs.

Adding at least 2,000 new guards along the U.S. Mexico border.

Conducting a complete review of immigration laws and policies.

Initial reaction to the proposals from groups interested in the issue was critical. The Mexican American Legal Defense Educational Fund called it "at best a patchwork compromise, which attempts to respond to a range of opposing points of view." It sanctions against employers, saying they would cause job discrimination against Hispanies. It also opposed the Jan. 1, 1970, residency cutoff date for eligibility for permanent resident status.

Given the complexity of the issues and the controversial nature of many of the proposals, it is not considered likel that Congress will enact the President's program this year.