El Salvador's National Police, in response to questions by the U.S. Embassy, today acknowledged the detention of two prominent leaders of the Lutheran Church here who had been missing since Wednesday. Police said they are under "investigation for subversion."

The two--who include the top Lutheran official in El Salvador--had not been heard from since Wednesday afternoon when they disappeared near the El Salvador International Airport, in the same area and under circumstances similar to those in which four American Roman Catholic churchwomen were abducted and killed in 1980.

The men being held are the Rev. Medardo Gomez, 37, president of the Evangelical Lutheran Synod of El Salvador and also pastor of Resurrection Lutheran Church here, and Dr. Angel Ibarra, 26, director of medical services for the Lutheran Church in El Salvador.

Salvadoran authorities have given no details of where or when the arrest was made or the subversive activities of which Gomez and Ibarra are suspected.

The families of the two Lutherans said today they have no idea how long Gomez and Ibarra will be held.

The U.S. Embassy here, notified of the case yesterday, contacted Salvadoran officials, including President Alvaro Magana, to press for information about the churchmen. Although both are Salvadorans, their activities are financially supported by American Lutheran groups and they have an affiliation with the Missouri Synod of the Lutheran Church, according to church sources in the United States.

After learning that Gomez and Ibarra were detained and not dead, friends and relatives filed a writ of habeas corpus to obtain their release. The document speculated that the subversive acts for which they were arrested consisted of visiting a Lutheran-run refugee camp near here with two visiting officials of the Norwegian Lutheran Church's aid program and then taking the Norwegians to the airport for a flight to Managua.

"The police would have considered that as a contact" with the guerrillas, one relative of Gomez said bitterly, referring to the visit to the camp, a facility for displaced persons operated by Gomez's Resurrection Church near the town of Nejapa, north of the capital.

One source familiar with the case suggested that Ibarra was under investigation for possible connections with the Communist faction of the guerrilla movement, but this could not be confirmed independently.

"This detention is illegal. No charge exists at all," said a lawyer working with Gomez's family who asked not to be identified.

The lawyer said that until the American Embassy and Lutheran Church officials in the United States put pressure on the government here, none of the security forces would acknowledge the detention of the two men.

The Lutheran presence is small in this predominantly Roman Catholic country. There are an estimated 2,400 church members in seven congregations in El Salvador.

The Missouri Synod of the American Lutheran Church is the most conservative Lutheran denomination in the United States, and it traditionally has avoided overt political activities here.

The Rev. Edward A. Westcott Jr., head of the Missouri Synod's board for mission services, said that Gomez had taken a "strictly neutral position in the struggle" among various political factions here and that the two officials had made no political distinctions in providing humanitarian services to anyone asking for help.

In December 1980, two American nuns returning to their missionary work here from Managua were picked up by another nun and a lay worker at the same airport, near which they were seized and murdered, allegedly by members of the Salvadoran security forces, according to court records here.