President Carter said yesterday he is "seriously concerned" about interference in the Dominican Republic's presidential election and warned Dominican authorities that U.S. support "will depend upon the integrity of the election process."

Carter's statement came against a background of guarded, but increasing optimism in the administration that the Dominican armed forces are backing away from their apparent attempt to tamper with the election results.

Reliable sources said that, while the outcome is still far from clear, the administration's most recent intelligence indicates that President Joaquin Balaguer and the Dominican military commanders will permit an honest vote acount and allow the victorious candidate to take office.

The military forcibly halted ballot counting early Wednesday after returns showed Antonio Guzman, Balaguer's left-of center challenger, wih a 3-to-2 lead. That triggered fears of a military attempt to keep the conservative Balaguer in office.

Since then, the United States has been putting heavy pressure on Balaguer to honor his pledges of a free and honest election. Carter's public statement, which was decided on after intense debate in the administration, was described by one U.S. source as "the biggest shot in our locker."

In his brief statement, the president said: "I retain my hope that the legally constituted electoral authorities in the Dominican Republic will be able to carry out their responsibilities without interference and that the outcome of the elections will be respected by all."

He concluded, "The degree of our country's support for the Dominican government will depend upon the integrity of the election process."

Reliable sources said the statement, which was rewritten several times, was intended to convey an unmistakably tough message without treading on the sensibilities of the Dominicans about U.S. interference in their internal affairs.

For that reason, the statement took pains to point out that Carter had been in touch with some Latin American leaders. The sources said he had consulted the presidents of Venezuela, Colombia, Panama and Costa Rica and the secretary general of the Organization of American States, Alejandro Orfila.

Carter also stressed that U.S. officials would carefully examine the report of the three former Latin American presidents who acted as OAS observers in the Dominican election.They are Galo Plaza Lasso of Ecuador, Julio Cesar Mendez Montenegro of Guatemala and Misael Pastrana Borrers of Colombia.

The three returned to Washington yesterday and released a report that diplomatic sources said would add to the pressure on Balaguer and the Dominican military for an honest count.

Although it was couched in circumspect language that avoided pointing a finger at anyone, the report expressed dismay at the interruption of the vote counting process and called on Balaguer to "dispel the doubts that have cast graves shadows over the integrity of his country's institutions."

For Carter, the Dominican situation is especially troublesome because he has praised Balaguer publicly as an outstanding democratic leader.