Secretary of State George P. Shultz, saying that world peace requires "rapid restoration of economic growth," today called for "special, urgent emphasis on reducing barriers to North-South trade through mutual exchange of concessions."

In a speech to the Foreign Policy Association, Shultz said that "the name of the game right now is economic growth," that "world trade is the key to this process" and that the General Agreement on Tariffs and Trade (GATT) should be "the engine of the coming recovery."

"Preparations should begin now for a new effort of trade liberalization in the GATT, with special, urgent emphasis on reducing barriers to North-South trade through mutual exchange of concessions," he said.

Answering questions afterward, Shultz called anew for Syria to remove its forces from Lebanon.

In an implied rebuke to Arab leaders who are demanding Israel's withdrawal, he said "there's an opportunity there" for them to persuade Syria to cooperate. He challenged the Soviet Union to pull its arms and troops out of the Middle East and countries such as Afghanistan.

But the emphasis of Shultz' speech, the longest and most detailed he has made since assuming office, was on arguing that the industrial nations and the Third World have a common stake in working together to end the world recession.

"The reality of mutual interest between the Northern and Southern Hemispheres is not at all reflected in either the doctrinaire Third World theory of debilitating dependency or the aid-givers' obsolete sense of patronage," he said.

"There is now a relationship of mutual responsibility . . . the reality of North and South is now that all of us are in one boat. We are all looking for a rising tide and calmer seas to speed us on our course."

His message, delivered on the eve of the economic summit, which begins this weekend in Williamsburg, Va., reflected Shultz' conviction that peace and stability depend, in great measure, on creating prosperity for all nations.

That conviction has been reinforced by the threats of bankruptcy to such countries as Poland, Yugoslavia, Mexico, Brazil, Argentina and Nigeria. Shultz cited with approval the austerity measures taken by these countries with U.S. encouragement, but he added:

"Austerity alone cannot be a sufficient solution when so many countries are in trouble. If everyone practices austerity and cuts imports, this only chokes world trade and spreads the hardship further. The ultimate objective must be growth, not austerity."

He gave no specifics about what concessions on trade liberalization the United States would like to see adopted in the GATT. But he warned, in almost passionate terms, against the dangers of listening to those in various countries who would make protectionism "intellectually respectable" and portray it as "a virtue."

Shultz, who is credited with bringing President Reagan to a more sympathetic view of foreign aid and Third World cooperation, listed three areas of U.S. policy emphasis:

* "Patient support for social and economic reform and for the strengthening of free political, economic and social institutions."

* "Security assistance to help insure that the process of democratic evolution is not disrupted or overwhelmed by armed minorities backed by external powers and alien ideologies."

* "Leadership in international trade and financial cooperation to promote economic development and progress in the developing world."

In discussing the Middle East, he said Syria's interests would be better served if Lebanon was "a stable, prosperous neighbor" rather than a country partitioned through foreign occupation and internal feuds.

Referring to the fact that Israeli withdrawal depends on Syria's willingness to pull out its forces, he said: "For those who feel especially strongly that Israel should get out, well, there's an opportunity there. All you have to do is get the Syrians to leave."

Asked about the Soviet role in the Middle East, Shultz replied: "I would think that if the Soviet Union gets its arms not only out of that area and other areas and gets its troops out of places like Afghanistan, it would contribute a lot to stability."