The people of Puerto Rico have fired a salvo at the U.S. Navy in a continuing battle over the military's use of tiny Caribbean islands for target practice.

The governor of the commonwealth and the mayor of the island of Vieques filed suit late Wednesday against Secretary of Defense Harold Brown and several high Navy and Marine officials. They claimed that the Navy has violated a number of environmental laws by bombing and strafing Vieques and its surrounding waters.

A similar controversy arose over the Navy's bombing of Culebra, a nearby island, a few years ago.

The suit asks that the U.S. District Court in Puerto Rico stop the Pentagon from continuing such operations, including a large-scale exercise called Solid Shield 78 scheduled for May, until the proper permits and environmental impact statements are filed.

Louis Rivlin, an attorney for the islanders, said in a telephone interview yesterday that the Navy had stepped up its bombing and shelling around Vieques after agreeing to stop the same activities around Culebra in mid-1975.

"The governor (Carlos Romer-Barcelo) has been talking to the Navy about this for some months without satisfaction," Rivlin said. "We felt the suit was the only way we could feel confident in foreclosing this huge '78 exercise."

A spokesman said the Navy had not yet seen the suit and therefore had no comment.

Vieques, lies about 20 miles long and 4 miles wide, just off the southeast coast of Puerto Rico. It has a population of about 7,000, according to the suit, and 70 percent of it is owned by the Navy.

According to Rivlin, a group of fishermen on the island have long been complaining about the Navy's stepped-up operations around the island because their fishing waters are put off-limits during firing exercises.

The continued bombing, strafing attacks, and amphibious landings by the military have caused water, air and noise pollution, the suit alleges.

Cattle have been killed by some shells, and the combined operations have resulted in "irreparable damage to the ocean waters, the coral reefs, mangrove swamps, rare phosphorescent bays, beaches and bluffs of Vieques," the suit contends.

Rivlin said that to his knowledge no residents of the island have been injured by the prolonged bombardment of the area. But the suit claims that the military operations "pose a significant hazard of immediate injury to residents of Vieques and longterm insidious risks to human safety because of the accumulation of hidden unexploded ordinance. . . "

In relying on the environmental laws as grounds for the action, the suit notes, for instance, that the definition of "pollution" in the U.S. Water Pollution Control Act includes "munition." In effect then, the suit argues that the Navy didn't get the required permit before discharging its "pollutant" bombs and artillery shells.

Vieques is about 10 miles from Culebra, the island site of a similar dispute between Puerto Rico and the Navy in the early 1970s.

The Associated Press reported from San Juan that local fishermen blocked Navy targets off Vieques with their boats last weekend. Two were arrested when they refused to leave a target area.