A Cabinet-level task force has recommended that illegal aliens who have lived for five years or more in the United States be permitted to remain as permanent resident sources confirmed yesterday.

In a report last week to President Carter, the group also suggested strengthened border controls, possible use of non-counterfeitable alien identity cards and civil sanctions against employers who knowingly hire any future illegal aliens.

Although the exact number of illegal aliens currently in this country is not known, U.S. Immigration and Naturalization Service officials have estimated the figure at 6 million to 8 million.

Many are believed to have been in the country for five or more years, but there is no reliable estimate of the exact number, officials said.

Legislation to curb illegal immigration has failed in Congress in recent years, but Carter promised action in his campaign, and has given the matter high priority since taking office.

The task force included Attorney General Griffin B. Bell, Secretaries of Labor Ray Marshall and Health, Education and Welfare Joseph A. Califano Jr. and Deputy Secretary of State Warren G. Christopher.

The amnesty for residents of five years or more was seen as a "reasonable midpoint" that would be both equitable and administratively manageable, one official said. Presumably the five years would be counted back from the date that legislation is passed, thus covering more workers the longer that enactment is delayed.

In addition to money for more manpower and equipment to block illegal entries, the group recommended long-range programs of economic aid, trade and investments to countries such as Mexico so that their residents would have less reason to escape to this country.