The Pentagon and State Department have recommended to the White House that there be no increase in the current limit of 55 U.S. military personnel training government troops in El Salvador, administration officials said yesterday.

The Pentagon had under study last month a proposal to raise the administration's self-imposed limit on advisers to 125. Gen. Wallace H. Nutting, former head of the U.S. Southern Command in Panama, said in an interview that 55 advisers were not enough. But a Pentagon-State working group decided not to forward such a recommendation to President Reagan, in part on grounds that Salvadoran troops can be trained in neighboring Honduras.

While the administration was moving to limit its land presence in El Salvador, it also was moving yesterday to reestablish a strong naval presence in Central American waters as the aircraft carrier USS Coral Sea and its escorts started patrolling off Nicaragua's east coast, and the battleship USS New Jersey steamed toward the country's west coast.

The Coral Sea replaces the carrier USS Ranger, which left Central American waters last week.

As the Coral Sea took up its position, U.S. reconnaissance planes picked out a Soviet freighter, apparently loaded with arms, headed toward the battle group in the Caribbean, officials said.

There was no indication that the battle group would move to stop the Soviet ship. On July 31, however, a U.S. Navy destroyer used what one official described as "polite harassment" of another Soviet freighter heading for Nicaragua, asking its captain for the ship's name, destination and cargo.

Although the recommendation to keep the number of trainers in El Salvador at 55 has not been presented to Reagan, administration officials said it is likely to be presented soon, and he is expected to accept it. There has been resistance in Congress to any increase.

The officials said the inter-agency review concluded that the new U.S.-run military training facilities and program in Honduras could be used for the stepped-up training of Salvadoran soldiers, and that there was no need to increase U.S. military presence inside El Salvador.

The report recommended, however, that the definition of what constitutes a U.S. military "trainer" be tightened, so that more trainers can be sent to El Salvador without bringing back other personnel.

Officials said some of those currently counted as trainers--a dozen or fewer--are communications or administrative specialists. These will be reclassified, leaving room for a slight increase in those working with the Salvadoran army on the problem of how to fight the leftist guerrillas there without killing civilians in the process.

On July 24, The New York Times, citing senior administration officials, reported that the Defense Department had recommended to Reagan that he raise the adviser level to 125 next year.

Reagan, in a news conference, denied that any such recommendation had come to him, and White House officials still insist that they never saw such a Pentagon recommendation nor was one presented to the National Security Council. But Senior Pentagon officials said that such an increase was under consideration in the Defense Department.

As administration officials explain it, it was decided July 8 at a National Security Council meeting to ask the Pentagon, State Department and others to review various options--such as naval maneuvers and military exercises--to keep pressure on the leftist Sandinista government in Nicaragua, which is supporting rebels in El Salvador, and to show American resolve in combating insurgents in the region generally.

An increase in training personnel in El Salvador was explored as part of that review, but ultimately rejected it.

Officials declined to say whether political considerations played a part in this decision. As details of the administration's muscle-flexing plans leaked out in July, they caused some alarm in both Congress and Latin America. Officials did say that the State-Defense review team recommended increased consultation with Congress before future decisions are made to expand U.S. military activity in the region.

The administration also has decided for now not to let U.S. advisers spread farther into the countryside with Salvadoran units. This was recommended by some military specialists, but the Pentagon rejected it.

The Defense Department said yesterday that the U.S. military presence remains about the same as it has been for months in El Salvador: 49 trainers working with Salvadoran troops; five military specialists at the U.S. Embassy and 26 medical personnel.

In Honduras, the Pentagon said, the number of U.S. military people is increasing to prepare for the main part of the training exercise there. The count given yesterday for U.S. personnel in Honduras was 129 trainers at Puerto Castilla, 76 trainers across the country, 60 Air Force people at the radar site at Tegucigalpa and seven specialists attached to the military group at the U.S. Embassy.