Secretary of State Alexander M. Haig Jr. today told the developing nations that dominate the United Nations General Assembly that the United States is committed to a "new strategy for growth" to assist the world's poorer countries.

In a prelude to the North-South summit meeting at Cancun, Mexico, a month from now, Haig called for "immediate international attention" to three areas: global expansion of trade, an increase in private investment and international cooperation in food and energy.

He unveiled no details, but said that specific proposals will be announced when President Reagan joins 21 other chiefs of state or government at Cancun, a Mexican resort. Haig said the United States will attend the meeting "in a constructive and cooperative spirit."

With Soviet Foreign Minister Andrei Gromyko looking on from his General Assembly seat, Haig attacked the Soviet occupation of Afghanistan and the Vietnamese occupation of Cambodia as among "the greatest dangers" to the U.N. charter and the process of economic development.

"The world's hopes for peace, for security and for development will be jeopardized if 'might makes right' becomes the law of nations," Haig said.

In a preview of his scheduled meetings here with Gromyko Wednesday and next Monday, Haig formally tied arms control agreements to Soviet actions in regional conflicts. Such "linkage" -- which has been rejected in the past by the Soviet Union -- is a central feature of the Reagan administration's policies toward negotiations with the Soviets.

By far the greatest part of Haig's address dealt with world economic development, a favorite subject of the Third World majority in the General Assembly. Haig's decision to devote most of the annual U.S. policy address here to economic rather than military or East-West political issues was described by aides as an effort to assure developing countries that the Reagan administration is responsive to their needs and concerns.

Haig went to great lengths to portray the United States as remaining in the mainstream of traditional international economic policy in several respects. He described the United States under the Reagan administration as backing free trade and open markets, resisting protectionism and supporting foreign aid through bilateral programs and international development banks.

He gave new emphasis on private economic cooperation such as the U.S. plan for development of Jamaica and U.S. business ties with Southeast Asian nations. He also called for economic development "through reliance on incentives for individual economic performance."

At the same time he criticized anticapitalist policies by saying that "suppression of economic incentives ultimately suppresses enthusiasm and invention. And the denial of personal freedom can be as great an obstacle to productivity as the denial of reward for achievement."

Haig, who plans to spend more than a week here meeting Gromyko, Western European foreign ministers and groups of senior diplomats from Asia, Africa and Latin America, spent most of his day in diplomatic meetings.

He lunched with British Foreign Minister Lord Carrington and met the chief diplomats of Australia, Italy and Japan as well as U.N. Secretary General Kurt Waldheim.