One of Ronald Reagan's closest business advisers is urging him to launch the country on a new "national resolve or mission" -- on the scale of the space program in the 1960s -- to help the economy recover and restore America's technological competitiveness.

William M. Agee, chairman of the Bendix Corp., also is calling for a sharp increase in U.S. economic aid -- and attention -- to less-developed countries, possibly in the form of a modern-day Marshall Plan, to help the Third World get on its feet.

And, while strongly endorsing Reagan's announced plans to slash spending and excessive government regulations, Agee rejected the notion that the new president-elect should "roll back" health, safety and environmental programs entirely, as some conservatives have suggested.

He also asserted that business must keep up its recent efforts to display a "social conscience" -- by continuing existing affirmative-action programs and attempts to clean up the environment.

One of Reagan's earliest and most avid supporters, Agee made his remarks in a 1 1/2-hour interivew in his office at Bendix headquarters here, during which he discussed a broad range of business and political issues. Excerpts of the conversation appear on Page F3.

Clearly delighted at the Californian's recent landslide victory, Agee said the new administration must act "fairly quickly . . . and decisively" to develop a long-term plan for getting the nation back on track again, boost defense spending sharply and cut taxes for individuals and business.

He also detailed reasons he believes U.S. competitiveness has slipped in recent years, opposed government subsidies, such as the Chrysler loan-guarantee program and auto-industry requests for import quotas, and conceded American business has a lot to learn from Japanese managers.

Agee offered no specific suggestions for a new 1980 counterpart of the space program, but he said whatever the new administration adopts should have the potential for the same kind of "technological fallout" that the moon-shot program provided for industry to use.

He also suggested that because of this and mounting defense priorities, the government may want to scale back its commitment to the crash synthetic fuels-development program that President Carter recently pushed through Congress.

Agee said his call for a new Marshall Plan for the Third World was based on economic self-interest as well as concern. He argued that the health of developing nations was "absolutely critical to allow the total world economy to grow during the next 10 or 20 years."

However, the Bendix chairman cautioned that money alone would not be enough in the push to make developing nations viable partners in the industrial-world economy. He said U.S. business also must reach out and foster "a climate of friendship" with Third-world countries.

Talking frankly about the problems of American business, Agee showed himself a vigorous advocate of increased economic incentives for U.S. corporations, from a reduction in overall tax burdens to stronger tax write-offs for investment in new plant and equipment.

At the same time, however, he conceded that at least part of business' current problems stemmed from plain bad management decisions. He said too many executives think far too much about short-term profitability and not enough about long-term goals.

Agee said he worries sometimes whether business will be flexible enough to meet new demands, but added he was confident the new crop of executives will be able to pull through.