The Reagan administration, concerned about continuing domestic and foreign hostility toward its controversial involvement in El Salvador, is mounting a new offensive to build public support for its policy of backing the Salavadoran junta with U.S. arms, money and military advisers.

The first trial probe of this new public relations effort is expected to come in a speech by the new assistant secretary of state for inter-American affairs. Thomas O. Enders. Although the State Department said yesterday that Enders plans a speech on El Salvador in the near future, it gave no further details.

However, it is known that tentative plans are for Enders to give the speech before the Washington World Affairs Council within the next week or two.

According to administration sources, the speech, as tentatively contemplated, would have three main goals: to start building a constituency for the administration's policy among leaders of the U.S. foreign policy establishment, to counter foreign suspicion that has been stirred up by criticism from the new Socialist government in France, and to give a new demonstration of support to the junta's civilian president, Jose Napoleon Duarte, who faces increasing difficulties with El Salvador's political rightists.

The idea had been opposed by some key administration officials, who think that the best approach is to continue a low profile on the Salvadoran situation to avoid renewed debate about whether the United States is supporting a repressive regime and heading toward a Vietnam-type involvement. However, the sources said the debate apparently has been resolved in favor of using the Enders speech as a vehicle for what is likely to be billed as "a major policy statement" on El Salvador.

Underlying the decision is an awareness of suspicion and concern among Americans about U.S. Salvadoran policy. That awareness, the sources said, has been reinforced by opinion polls and by the observations of administration officials who have encountered hostility to the policy at universities and who have found other potentially neutralizing groups like the business community unwilling to take a lead in supporting the policy.

In dealing with the criticism, the administration initially took the tack, articulated most forcefully by Secretary of State Alexander M. Haig Jr., that it was drawing the line against subversion in the hemisphere by the Soviet Union and Cuba. However, that effort only generated more controversy, particularly after a State Department white paper detailing alleged communist aid to the Salvadoran insurgents was criticized for errors and inconsistencies.

During recent weeks, the administration has said as little as possible about the situation. It even has put on the back burner, at least for now, a projected new white paper that had been conceived as justifying its evolving Caribbean basin policy by detailing the extent of alleged communist activity in the region.

However, some administration officials believe that successful pursuit of U.S. goals in the hemisphere requires a new effort to build domestic support. Those in this camp argue that the time to start is now, when the university campuses -- the centers of protests over El Salvador -- are in summer recess and when it might be possible to mobilize business and civic groups as a counterforce.

These officials also are concerned about the position of the Socialist government of French President Francois Mitterrand, which advocates a political solution in El Salvador that would involve concessions to the leftists and could stir up anti-junta sentiment in Western Europe. This could shatter the facade of support that America's allies have given to Washington's involvement in El Salvador.

Finally, there is concern that renewed activity by the Salvadoran right could hamper Duarte's efforts to bring about promised reforms, isolate him from the military, whose support he needs, and make him vulnerable to ouster. For that reason, some U.S. officials believe that a strong, high-level reiteration of Washington's support for Duarte is imperative now.

That is what prompted the idea of a speech by Enders designed to address these considerations. Advocates of this approach are understood to believe that such a speech, while pointing out anew the alleged Cuban threat, should downplay the Cold War rhetoric originally used by Haig and put the main emphasis on U.S. support for Democratic reform and economic progress in El Salvador and the Caribbean region.