Future problems between the United States and Mexico can be averted or resolved only if there is a better understanding between the two neighboring nations.

This was the message stressed in an interview with Agustin Legorreta, chairman of the board of Banco Nacional de Mexico, the oldest bank in Mexico.

"To think that we can solve every problem is impossible and naive," he said.

Legorreta was in Washington last week for the opening of an exhibit of 19th-century Mexican paintings sponsored by Fomento Cultural Banamex and Banamex Cultural Foundation, organizations created by the bank to promote Mexican culture both in Mexico and the United States.

The recognition of cultural ties and differences between the two countries is one step toward cooperation in other areas, Legorreta said.

"We feel that culture is a particularly important link in the understanding and knowing of each other," he said. "It's hard to know another nation if you don't have an understanding of its culture.

"We are the first to try and bring Mexican culture physically to the United States in an organized and planned manner. In the future, others will follow in the same way."

Legorreta said that the feeling in Mexico toward the Reagan administration "is one of optimism" and expressed the hope that there "will be a chance to restart talking on many subjects." U.S. relations with Mexico soured during the Carter administration when a dispute arose over the pricing of Mexican natural gas headed for the United States.

Mexico is using its new-found oil wealth to rebuild the country's social and industrial infrastructure, Legorreta said.

"Oil is not the solution to our problems," he said. "It is an enormous help. It removes one of the everpresent limitations of developing counties -- the need for hard capital."

The bank has been active in promoting industrial investment in Mexico. Legorreta said there is an effort under way to attract more manufacturing activities with the goal of providing more jobs and redistributing income more equitably. "Jobs are the great equalizer," he said. "And oil is accelerating that process."

"We have a very good [industrial] base to project ourselves into the future," he said.

Legorreta said that high interest rates in the United States have pushed rates up in Mexico or the country would risk on outflow of capital. The high interest rates have made it more difficult to service Mexico's foreign debt, he said.

The Mexican banking system has been growing at a healthy rate of 30 percent over the past four years, increasing the financing capacity, Legorreta said. Banco National, with 600 branches throughout Mexico, has total assets of $13 billion and employs 24,000 persons. With representative offices in Tokyo, Paris and Madrid and a branches in London and Nassau, it does more international business than any other bank in Mexico.

Recent agreements by international lending and financial institutions. World Bank

A credit of 32.6 million in special drawing rights ($40 million) from the International Development Association, a World Bank affiliate, for an agricultural credit project in Bangladesh. The project will, over a four-year-period, establish a reliable long-term credit system, and increase agricultural production, incomes and employment opportunities in five districts of the Rajshahi division of northwest Bangladesh. The funds will help provide credit to farmers for the installation of shallow tubewells, the construction of foodgrain storage facilities, the purchase of equipment and tools and the equipping of workshops for the maintenance of irrigation facilities.

An IDA credit of 8.2 million in special drawing rights ($10 million) to Lesotho for a third education project. The project calls for the construction of about 150 primary schools; the provision of 1.9 million textbooks; and the provision of permanent facilities for a total of 235 trainees at two vocational training centers. Technical assistance to the Ministry of Education also is included to strengthen its planning division and statistics unit. International Monetary Fund

A stand-by arrangement for the government of Ethiopia, authorizing up to the equivalent of 67.5 million in special drawing rights over the next 14 months in support of the government's economic and financial program. The Fund has agreed to a purchase equivalent to 18 million in special drawing rights under the compensatory financing facility because of an expected export shortfall in the 12-month period ending in June, due mainly to a decline in world coffee prices.

An extended arrangement for the government of Zambia, authorizing purchases up to the equivalent of 800 million in special drawing rights over the next three years in support of the government's economic and financial program. The Zambian program is aimed at increasing domestic production and diversifying its structure, while moving towards domestic financial equiliburium and a sustainable external position. Export Impact Bank

A $3.8 million loan to the Electricity Generating Authority of Thailand, a government-owned utility, to support the purchase of $5.9 million in U.S. goods and services for a control and information systems for the company's Bank Pakong thermal power plant number two.