The United States has approved a Mexican request to purchase at least a dozen American supersonic jet fighters as part of new effort to modernize the Mexican armed forces, qualified Mexican sources reported today.

Mexico reportedly made the secret request for the F5 jet fighters four months ago. Although the State Department has refused comment, qualified Mexican sources said the United States recently approved the sale on Commercial terms. Under those terms the State Department must approve it, and Congress must be informed of the sale, although its approval is not needed.

Besides the new aircraft, Mexico has announced plans to used its growing oil earnings to buy armored vehicles, amphibious craft and heavy antitank guns. The purchases go well beyond military needs for keeping internal order, the main role of the Mexican Army up to now.

Because Mexico is proud of its civilian rule in a continent dominated by military, the question of arms spending causes embarrassment among officials and is treated with great discretion. The joint Army and Air Force budget this year was increased 54 percent to $1.1 million. Much of the increase, according to Defense Minister Felix Galvan, will be spent on new equipment.

Mexico's Air Force is composed of about 75 combat planes, most of which are from the 1940s and 1950s, according to the International Institute for Strategic Studies. The force includes 14 T33 jet trainers and five squadrons of propeller aircraft.

The decision to moderinize the 120,000-member armed forced also will mean the gradual abolishment of 23 cavalry regiments and the replacement of about 14,000 horses by armored cars and jeeps. Mexico already makes most of its own firearms and ammunition.

If it buys the F5 jets, it will have to expand one or more of its five military airfields. A team of U.S. advisers has been here to assess the changes required, according to Galvan.

Neither Galvan nor civilian politicians have spelled out the purpose of the jet fighters or other items on the shopping list.

The official reason given for the unprecedented budget increase is that Mexico needs to replace its obsolete arsenal. Many of its planes and tanks are of World War II vintage.

But Mexico has several reasons for the change in policy, local and foreign analysts report. Oil wells have given the country economic power and political clout, which the leadership believes should be backed by a more impressive military presence.

At the same time, the military clearly wants its share of the national pie that has grown with oil. By Latin American standards, defense spending here has been extremely low. In 1980, it was 1.1 percent of the nation's $73 billion budget.

The request for the sophisticated fighter planes and the anounced plans to modernize most of the country's military equipment has raised alarm among politicians and diplomats.

Among the gloomy scenarios envisaged by critics is the fear that Mexico may follow the example of other developing oil-producing countries that have heavily invested oil profits in arms. They believe that in a country, which for internal political reasons has always maintained a small army, a vast, modern arsenal would bolster the military's small political influence.

Moreover, the request for the F5 fighters raises the level of military sophistication in a region that is becoming increasingly unstable. No country in Central America or the Caribbean region has ever brought this kind of plane, with the exception of Cuba, which has Soviet supersonic Migs.

Defense analysts in Washington have privately said that supersonic fighter planes such as the F5, which can cost close to $5 million depending on the accessories, are an extravagance for this country. With the U.S. military might to the north and tiny Guatemala to the south, "Mexico can make no strategic argument that it needs such planes," one U.S. analyst said.

"Even if they buy twice as many planes, Mexico cannot defend the oil fields against sophisticated attack," he said."All they can do with them is fly them too fast over their own country or show them off with visits in Central America."

But Mexico has an added perception about its security that is growing along with its budding vision of itself as a political guardian of the region. As an example, officials here have been concerned by recent suggestions that Washington may renew military aid to Guatemala, which was suspended in 1977.

Mexico's relations with Guatemala, whose military governments it regards as repressive and futile, have been strained for some time. They became more tense whenever Guatemala reasserts it sovereignty claims on their neighbor Belize, which is expected to become fully independent from Britain later this year.

Although Mexico logically does not need to fear aggression from Guatemala, whose population is one-tenth of Mexico's 68 million, Galvan has talked privately about the need for Mexican air superiority as deterrent to Guatemalan saber-rattling.

Despite the U.S. assessment that supersonic jet fighters are strategically superfluous for its neighbor, the United States clearly has made an about face with its willingness to sell such advanced weaponry here.

In early 1978, when both Mexico and Guatemala sought to buy F5 jets, Washington refused the Guatemalan request in keeping with president Jimmy Carter's desire to reduce foreign military sales, especially to Third World countries. Not wanting to offend its sensitive neighbor with a refusal. Washington at the time stalled the reply to Mexico. Eventually, Mexico, which at the time also had serious financial difficulties, withdrew the request.

Mexico has been courted by arms salesmen ever since it moved into the ranks of big oil producers, and manufacturers from Spain, Brazil, France, the United States, West Germany, Britain and Israel have been pushing their hardware here.

In Paris last month, Galvan reportedly ordered about 50 armored vehicles from the Panhard company. In Tel Aviv, by his own account, he decided against buying Kfir fighter planes, and in Madrid, he reportedly placed an order for six Coast Guard cutters to keep poaching fishermen out of Mexican waters.