The Carter administration has promised further review - but no definite action - on complaints from the $160-million-a-year Florida tomato industry that it is being run out of business by Mexican imports.

Florida growers and their representatives testified in March before the Senate subcommittee on foreign agricultural policy that they had been forced to sell their tomatoes for less than they cost to produce because of an inundation of Mexican vegetables.

Subcommittee Chairman Sen. Richard (Dick) Stone (D-Fla.) said the Mexican imports posed a question of "survival" forrr the industry of his home state.

However, administration officials who testified before his subcommittee last week indicated they did not plan any quick action against the imports.

The tomato controversy comes at a time when the administration is also studying complaints from the sugar, meat, potato and dairy industries regarding the impact of imports. The United States, with a foreign food bill of more than $10 billion a year, is the world's leading food importer.

Officials said here last week that tomatoes illustrate the difficulty of taking tough action against such imports.

First, the administration is committed to fight against inflation in food prices. Florida and Mexico supply 75 percent of the nation's tomatoes, a figure which increases to 99 percent in winter. Therefore, any controls would likely increase prices. This, in fact, is what the Florida producers want.

Second, the administration wants freeragricultural trade.

Testifying before Stone's subcommittee last week, Leo V. Mayer of the special trade representative's office noted that the Carter administration is making a "maximum effort" at multilateral trade negotations in Geneva to "reduce the numerous trade barriers imposed by other countries against U.S. exports."

The country last year exported nearly $30 billion worth of food. The nation's corn industry is seeking a reductimn of European trade barriers, to let more U.S. feed grains into Europe.

In 1977, the United States sold slightly more goods and food to Mexico than vice versa: $4.8 billion compared with $4.7 billion.

Officials of the Department of Agriculture say they share the concern of Florida growers. The devaluation of the Mexican peso has recently given Mexican growers an edge in the U.S. market. Florida growers suffered from a killing frost in 1977, and from more trouble with the weather this year.

Some agricultural economists say the situation of Florida growers may improve if the weather is normal this year. They note that, despite the difficulties, Florida growers share of the national tomato market has declined only from 33 percent in 1968 to 30 percent in 1977. Tomato acreage in Florida has remained fairly stable over the last few years.

Jose Carlos de Saracho, whose National Union of Vegetaoble Producers represents 20,000 Mexican growers employing 250,000 workers told the Stone subcommittee in March:

"My countrymen need jobs, even though the work that must be done is hot, dirty, backbreaking and hard."

U.S. officials, commenting on that, said they were concerned that if jobs are lost in Mexico more unemployed Mexicans will become illegal immigrants in the United States.

"We have to see this in terms of the broader immigration issue," said one official.

Florida growers want the government to require Mexican produce to be labeled as such in U.S. retail stores.

A bilateral working group is to meet June 14 and 15 to discuss the tomato issue. The consultations eventually could lead to voluntary restraints on the Mexican vegetable exports or, is warranted, U.S. import quotas. However, officials said tha tthe June meeting is "preliminary."