A national group of business and education leaders said yesterday that the private economic sector should do more to develop jobs for the hard-core unemployed, and that the federal government should do more to help the private sector provide these jobs.

The group, the Committee for Economic Development, made its recommendations in an 87-page report entitled "Jobs for the Hard-to-Employ: New Directions for a Public-Private Partnership."

Many of the recommendations contained in the report are not particularly new, according to government sources and manpower development officials. But the sources said the report is significant because it shows that private industry and commerce - frequently accused of being more interested in profits than social welfare - are beginning to take some initiative in solving problems traditionally handled by governmental agencies.

But, according to the CEID report, "greater reliance on the private sector" in helping to end long-term unemployment "will not be easy to achieve."

Federal tax and minimum wage laws, "undue" financial burdens "placed on firms' regular profit-making operations" by government-backed job training programs, "disappointment with particular program results, and impatience with the red tape and lack of stability in the funding and management frequently connected" with those programs have dampened private sector interest in job development, the report said.

But the report said business can no longer afford to take a lukewarm interest in developing jobs for the hard-core unemployed - many minorities, young and middle-aged people who have never held jobs or who have been without work for 15 weeks or more.

Why? Besides the "social and human costs," high unemployment is not "sound business practice" or "good public policy," the report said.

Also: "There is increased concern that without greater private involvement, the current rapid expansion in public training and employment programs could lead to excessive increases in public sector employment and spending and add to inflationary risks. At the same time, the feeling is growing that greater reliance on training and employment-creating activities in the private sector may in many cases prove to be more efficient and less costly," the report said.

In recommending steps the federal government could take to improve private sector involvement in job development, the committee noted in its report that "of the total $11 billion [federal] budget program devoted to employment and training in fiscal 1978, less than 10 per cent is scheduled to be devoted directly to private sector programs."

"We believe that this proportion should be significantly enlarged," the committee said, without specifying how much of an increase in federal job-training funds should be given to business and commerce.

Other committee recommendations:

Encouraging the private sector to develop "well-organized business community" job-training groups to "manage the community's federally supported on-the-job training contracts."

Such groups would be more capable of providing a wider variety of training services, cutting through the bureaucracy, reducing training costs and increasing business participation in job development programs, the report said.

Increasing incentives for private employment and training of the hard-core unemployed "through experimentation with tax credits and stipends for trainees and apprentices and wider use of selective . . . exemptions from the minimum wage."

The committee said minimum wage laws, which mandate a minimum salary of $2.65 an hour, are among a number of existing laws and regulations which "reduce employers' demands for labor by increasing labor's price." However, the committee cautioned that careful study should be made to determine the possible adverse effects of changing such laws and regulations.

Improving government employment and training programs - many of which, according to the committee, are affected by "nuclear policy direction, overlapping and uncoordinated administrative structure and bureaucratic inflexibility."