John Gavin, American ambassador to Mexico, says the United States and Mexico are close to initialing agreements that would increase free trade between the two nations.
According to trade officials, the most important of these agreements would require Mexico to cut export subsidies that give it what are regarded here as unfair advantages over American businesses.
In return for such a cut, the officials say, the US is promising to provide an ''injury test'' for Mexican exports that now face countervailing duties and litigation in the United States. As it is, US businesses can retaliate against subsidized Mexican exports without having to prove or allege injury to themselves from the competition.
Ambassador Gavin participated in three days of talks held here last week between President Reagan and Mexico's President Miguel de la Madrid Hurtado. Many of the news reports concerning those meetings pointed to disagreements between the US and Mexico over Central America. But Gavin said substantial progress was made in a series of talks concerning trade and investment policies and that the two sides reached a better understanding on Central America as well.
Mr. Gavin said that Presidents Reagan and de la Madrid got along ''famously'' in their meetings.
Gavin said he thought that Reagan succeeded in reassuring de la Madrid that the US ''truly supports'' efforts being made to resolve the Central America conflict by the Contadora group of nations which includes not only Mexico but also Colombia, Panama, and Venezuela.
But Gavin cautioned that the trade and subsidies agreements which US and Mexican representatives have reached must now be subject to a process of consultation with the Congress and with the private sector.
''We have to be sure that the Congress feels truly consulted and that they're aboard,'' said Gavin in an interview conducted at the end of President de la Madrid's visit here. ''The same thing is true for the private sector.''
Gavin acknowledged that there is a disagreement with Mexico over the means of achieving agreed-upon goals in Central America. He said the disagreement centered on the nature of the Sandinista regime in Nicaragua, which Mexico has provided with considerable support.
The Mexicans, said Gavin, exhibit a tolerant attitude, arguing that the Nicaraguan revolution should be given a chance to mature.
''We don't believe that the Sandinistas have given any indication of getting within 10,000 miles of keeping the promises they made'' to allow democratic freedoms and political pluralism, said Gavin, explaining the American attitude.
The ambassador praised Mexico and its President for undertaking ''heroic'' belt-tightening measures as part of a stabilization program agreed upon by Mexico, the US, and the International Monetary Fund, as well as by central and private banks. As a State Department reference paper explains it, the program has ''required significant sacrifices by all sectors'' of Mexican society.
''The Mexicans have bitten a couple of hard bullets,'' Gavin said. ''And last year they reduced their deficit as a percentage of gross domestic product, bringing it down from about 18 percent to 8.7 percent.''
''The Mexicans are making some very significant progress, which, by the way, Argentina is not,'' the ambassador added. ''The Mexicans were very helpful in assisting and structuring that rescue for Argentina, but what good is the rescue if it's just going to require another one several weeks and months down the pike - and another one and another one?''
The Mexicans' stabilization program is of more than academic interest to the United States. The US is Mexico's main trading partner, and Mexico is the third-largest trading partner for the United States, after Canada and Japan. But according to Gavin, a $32 billion decline in US trade with Latin America over the past two years has cost the United States some 600,000 jobs.
The most important of the tentative agreements now reached between the US and Mexico is a subsidies agreement consisting of more than a dozen pages of text. State Department, Foreign Ministry, and trade officials from both sides worked intensively on this agreement while President de la Madrid was here.
''What we got was an agreement which is a whole lot better than anything we thought we could get just a year ago,'' said an official in the Office of the US Trade Representative who helped to draft the agreement.
As the official described the new agreement, it will reduce the uncertainty and vulnerability that Mexican products now face in US markets. But it will also require Mexico to eliminate all of its export subsidies, with the exception of one financing subsidy that would be phased out over a several-year period. The agreement is to cover a three-year period.
Ambassador Gavin was asked to describe the most difficult problems facing Mexico in the coming years.
He replied that most important were ''structural problems in the economy'' and the restrictions these placed on coping with a rapid population growth, unemployment, and underemployment.
''You need 850,000 new jobs each year just for the young people coming into the market,'' Gavin said. ''It will soon be 900,000 a year, a million a year, and by the end of the decade, 2 million a year.''
''The economy right now is heavily weighted toward statal and parastatal organizations, as compared to the private sector,'' the ambassador said. ''In my experience, statals and parastatals do not create wealth or jobs.
''The problem is how you get all these statals and parastatals out of the businesses they're in and into the hands of the private sector and either make them efficient, productive, and competitive or close them down and spin them off.''