The Select Commission on Immigration and Refugee Policy yesterday recommended sweeping changes in national immigration laws, including making it a crime to employ an illegal alien, improved border controls and "amnesty" for the up to three million persons who illegally entered the United States before Jan. 1, 1980.

The recommendations were included in the final report of the commission, headed by the Rev. Theordore Hesburgh, president of Notre Dame. Taken as a whole, the commission proposals were designed to keep the door to legal immigration open, even widen it a bit, while clamping down harshly on border-jumping and other forms of illegal entry.

The report said there are anywhere from 3.5 million to 6 million illegal immigrants in the United States, more than half Hispanic, mostly from Mexico.

One key recommendation of the commission was substantial improvement of border control, with new planes, helicopters, better training and extra border guards (it said at any one time only 450 are on duty), which it estimated would cost about $45 million a year over the current $300 million spent on immigration enforcement.

A second method of deterring illegal immigration would be making it a crime, with civil and perhaps criminal penalties, to hire an illegal immigrant. The commission reasoned that would help close down the main economic incentive to illegal immigration.

The commission, however, failed to reach agreement on whether to require workers to carry tamper-proof identification cards, indicating their legal status in the country, which the worker would have to present when seeking a new job. Without such a system, Hesburgh argued, the ban on hiring an illegal would be too hard to enforce. But other members of the commission said the idea sounded too much like a police identification system, applicable to all workers, and blocked it.

In tandem with the new controls on illegal immigration, the commission recommended legalizing the status of those who entered before Jan. 1, 1980, on the theory that they constitute a workforce that can be exploited to undercut wage scales.

The commission recommended allowing immiediate relatives of U.S. citizens to continue coming in without quota restrictions. In addition, it said quotas applicable to other relatives and to any others who want to enter should be increased permanently from 270,000 a year to 350,000 with an extra 100,000 for the next five years to clear up waiting lists.

It recommended keeping the current 50,000 annual total for refugees but reached no clear guidelines on what to do about people seeking mass asylum, such as Cubans, except to say that those failing to meet normal asylum qualifications should be deported, or efforts made to get other nations to take them.