President Reagan's controversial hands-off policy toward new sugar price supports, already a source of concern among his own budget and foreign-policy advisers, now has drawn indirect criticism from seven Latin American sugar-producing countries.

In a formal letter to Secretary of State Alexander M. Haig Jr., ambassadors from the seven nations--all dependent on sugar sales to the United States--have warned that congressional approval of the price supports will adversely affect their economies and contribute to unrest or violence.

Their message went to the State Department as the House began gearing up for debate on a four-year farm bill that would reestablish a price-support program to prop up U.S. sugar producers.

Opponents, headed by Reps. Peter Peyser (D-N.Y.) and Margaret Heckler (R-Mass.), are expected to succeed in knocking the sugar program out of the bill when it reaches the floor. But the Senate included a sugar program in its bill last month, and industry lobbyists expect that a final farm measure will contain some type of sugar supports.

The U.S. sugar industry gained some unanticipated ground over the summer when Reagan, who had not endorsed a price-support scheme, agreed to accept whatever Congress produced in return for the votes of several key sugar-state legislators on his economic program.

Since then, however, as world sugar prices have continued on a downward trend, other administration policymakers have registered concern that a new sugar program could have costly budgetary and foreign-affairs consequences.

"Both the State Department and the Office of Management and Budget have become very concerned, even with the 18-cent-per-pound support price in the Senate bill, because of possible new costs to the government," a Department of Agriculture official said this week.

Sugar policy has been one of the more sensitive farm issues in the administration. After legislators and U.S. producers protested, the USDA earlier this year withdrew and has not republished an economic-impact study warning that a sugar support program could cost the government money and substantially intensify inflation.

Earlier last spring, another internal State Department study raised more storm flags over the cane, beet and corn sweetener industry. The study said developing countries that depend on sugar exports to the United States would be "greatly affected" by policies aimed at encouraging domestic production.

In lobbying for price supports, U.S. producers and sugar-state legislators have contended that, without the loan assistance, the domestic industry would continue to atrophy and the United States, which imports about half of its sugar, would become "hostage" to foreign producers.

But for the support program to work at little or no cost to the government, a system of quotas and duties would have to be established to limit imports. Such a system would protect U.S. producers by keeping lower-priced foreign sugar out while attempting to minimize government acquisitions of excess domestic production.

In their letter to Haig, the governments of Panama, Guatemala, Barbados, Honduras, the Dominican Republic, Peru and Nicaragua cautioned that quotas and increased duties on their sugar would seriously undermine their economies and work against the administration's professed policies of free trade and development stimulation.

Weakening of local economies, the letter said, could promote new social problems and restiveness, "creating and causing political tensions that are in many cases synonymous with violence."

A State Department official said yesterday the department could make no immediate comment on the seven nations' message.