In a rare display of official cooperation in a politically touchy area, U.S. and Mexican commerce ministers began a cross-country journey yesterday to sell Americans on the economic advantages of greater U.S. investment in Mexico and a free-trade agreement with that country.

Commerce Secretary Robert A. Mosbacher and his Mexican counterpart, Jaime Serra Puche, will meet this week with business and civic leaders in five U.S. cities to bolster the Bush administration goal of better trade and economic relations with the nation's southern neighbor and third-largest trading partner.

"Between us, we are going to be selling the advantages of a free-trade agreement that makes both countries more competitive," said Mosbacher, who has been pushing for closer political and economic ties with Mexico.

B. Timothy Bennett, vice president of the Washington consulting firm SJS Advanced Strategies, and a former U.S. trade negotiator with Mexico who now advises American and Mexican firms, called it "unprecedented" for a U.S. Cabinet secretary to tour the United States urging investment in another country.

"But if U.S. companies are going to invest in other countries, Mexico is the place where we get direct economic benefits," said Bennett. Mexico, he said, is a heavy buyer of U.S. products, with $7 of every $10 of its imports coming from the United States.

Mosbacher and Serra will be making their case in the face of scattered opposition from organized labor and some politically potent business and farm interests and their congressional allies.

Opponents argue that promoting free trade and investment with Mexico will take jobs away from American workers, especially at the low end of the wage scale, and will flood American shops with made-in-Mexico food and manufactured goods.

The tour will take Mosbacher and Serra to Houston, Dallas, New York, Chicago and Los Angeles, where Mexican-American business executives will be part of the targeted audience. Administration officials believe that the free-trade talks will spotlight Bush's interest in Mexico, which could deliver political gains for Republicans among the heavily Democratic Hispanic communities of California and Texas.

"If the Republicans play it right with the free-trade agreement, they could make a big killing," said George Munoz, a Chicago attorney who has been encouraging Mexican-American business executives to attend the Mosbacher-Serra appearance.

Economically, Munoz said, Mexican-Americans can gain from a free-trade pact by entering into joint ventures with small- and medium-size Mexican companies and helping giant U.S. corporations invest in Mexico.

Beyond improving U.S.-Mexican relations, the free-trade pact is widely seen as a Bush administration fallback if a troubled series of global free-trade talks fails to reach a satisfactory conclusion in December.

Bush has insisted that the Uruguay Round of global free-trade talks remains his top trade priority, and U.S. Trade Representative Carla Hills said a free-trade pact with Mexico will strengthen the global trading system, not be a substitute for it. Nonetheless, other countries fear that if the global talks fail, the result will be the creation of a large and wealthy North American economic bloc competing with rival blocs in Europe and Asia.

Bush asked Congress last month for authority to negotiate the free-trade agreement with Mexico, with congressional action on Bush's request due by spring and an agreement expected by the end of 1992.

Meanwhile, preliminary talks have begun, with the initial focus on whether Canada, which already has a free-trade agreement with the United States, should be allowed to join in to create a North American common market of 350 million people.