The Carter administration asked Congress yesterday to extend the government's main job creating program through 1982 and to revise it so that the number of public service jobs provided would rise or fall depending on the national unemployment rate.

Under the proposal to extend the Comprehensive Employment and Training Act (CETA), the number of public service jobs in the next fiscal year would be 725,000 the same authorized for this fiscal year.

Begining in fiscal 1980, the program would guarantee a base of 100,000 public service jobs a year plus additional jobs depending on the unemployment rate. For each one-half percentage point that the unemployment rate exceeded 4.75 percent, 100,000 more public jobs would be provided by the government, according to a trigger mechanism in the legislation.

For example, the unemployment rate currently is 6.3 percent. Under the proposed administration formula, that would mean about 500,000 public service jobs.

The formula would also mean that unemployment would have to be close to 8 percent - about what it was when President Carter took office - to maintain the current level of 725,000 public service jobs.

According to administration officials, it costs about $1 billion to provide 100,000 public service job slots.

Labor Secretary Ray Marshall, who with Vice President Mondale unveiled the proposal at the White House, said the legislation is designed to "target" government jobs programs on areas of chronic high unemployment and among the most economically disadvantaged persons.

Key members of Congress who attended the briefing generally praised the administration for its efforts, although none has read the legislation yet.

"The administration seems to be moving in the proper direction," said Rep. Augustus F. Hawkins (D-Calif.), whose employment opportunities subcommittee will hold hearings on the legislation begining March 1.

For the most part, the proposal would simply extend the major components of the GETA program, although it includes a slight increase in money for youth jobs. Overall, according to Mondale, the program would include $11.4 billion for jobs and training for more than 4 million persons during the fiscal year that begins Oct. 1.

Among the proposals in the administration legislation are:

The creation of local Private Industry Councils, made up of business and labor representatives, to provide local job training slots. The legislation includes an authorization of $400 million that administration officials said would be used for 100,000 job training slots.

A demonstration project involving 50,000 new jobs that would be used to test the jobs provisions of the president's welfare revision proposals.

Extention of the income limits on public service jobs applicants to cover all CETA public service jobs. Currently, the income level of about $7,000 a year for a family of four - above which an applicant is not eligible - applies to about half the 725,000 public service jobs.

The legislation also would impose for the first time a limit on how long a person could hold a public service job - 18 months during any given five year period. This is an attempt to deal with the issue of "substitution," under which local governments use CETA funds - earmarked as temporary help for the hard-core unemployed - to fill permanent public service jobs that should be paid for with local or state funds.

The 4.75 percent figures used in the legislation to trigger additional public service jobs is tied to the Humphrey Hawkins bill, which would set a national goal of a 4.75 percent unemployment rate by the early 1980s.

An aide to Hawkins said that while there may be some technical problems with the legislation, it generally followed suggestions to the Labor Department by the employment opportunities subcommittee.