Secretary of State Cyrus R. Vance said yesterday the United States must put priority emphasis on relations with developing nations our of concern both for their "harsh conditions of life" and future "peace and prosperity for ourselves.

In a speech to the National Urban League convention in Chicago, Vance concentrated on a subject to which he has been giving increasing attention in recent weeks -- the North-South dialogue between the industrial nations and the Third World.

In both public and private, Vance has said that he wants to spend much of his remaining time in office working on north-South problems, and last night he outlined why he believes the issue "requires much more attention -- and understanding -- than our nation has given it."

On the economic side, Vance noted that in each of several states -- California, Illinois, Michigan, Ohio, New York and Texas -- "20,000 or more jobs are derived from the production of manufactured goods we export to developing countries. All told, around 800,000 jobs in manufacturing alone depend directly or indirectly on exports to developing countries."

For the American consumer, he added, "some 93 percent of our tin, 85 percent of the bauxite from which we make aluminum, and all of our natural rubber are imported from the developing world. Over 40 percent of the petroleum we use comes from developing countries, and roughly half of these imports are from developing nations outside the Middle East, such as Mexico, Nigeria and Venezuela.

Referring to security questions, Vance said, "During the past three decades, armed conflict in the world has centered on problems involving developing nations. And it is a fact of modern international politics that the United States can best help resolve regional disputes in the developing world with the cooperation of the nations in the region. . . ."

To acheive these ends, Vance outlined a six-point strategy for dealing with the Third World economically and politically. In summary, his points were:

Greater economic cooperation between developed and developing nations, including making "the oil-producing nations recognize their responsibility for the consequences of their actions on the proper nations as well as on the industrial economies."

Working through foreign aid and other means to find "practical solutions to concrete development problems such as food, energy, health and education."

Consistent support of human right to encourage "democratic change and social and economic justice. . . without being diverted by the myth that if we encourage change or deal with the forces of change, we oly encourage radicalism."

Recognizing the difference between internal changes and threats to nations from outside forces and, despite U.S. reluctance to use military force, being prepared "to act forcefully when our vital interests, or the vital interests of our friends and allies are challenged by foreign threa!s."

Working "actively and patiently" for the resolution of regional disputes, such as "a comprehensive settlement" of the Arab-Israeli dispute in the Middle East and "peace and racial justice in southern Africa."

Being prepared "to work with any nation if it is prepared to work with us toward common practical goals and not allowing "real or imagined ideological differences to prevent our cooperation with others in finding negotiated solutions to armed conflicts or other major international crises."