Ambassador Jorge Luis Zelaya Coronado, who had been conducting a campaign to improve his country's relations with Washington, was summoned to the State Department last week to be given a protest over the handling of an arrest of a U.S. citizen, the State Department confirmed yesterday.

Robert Ryan, deputy assistant secretary for inter-American affairs, protested Guatemala's failure to allow a U.S. consul to see the American, Michael Ernest, within 48 hours as required by international law and asked that due process be followed in the case, a State Department official said.

Diplomatic sources said U.S. officials also have told Guatemala of their concern about the death sentence imposed on four men convicted of guerrilla activity in a non-public trial. A Guatemalan diplomat said the sentence was on appeal.

A source on Capitol Hill said the arrest of Ernest and the planned executions will give "great impetus" to a resolution signed by 83 congressmen at the end of the last session asking that the sale of spare parts for Guatemalan military helicopters and planes, authorized by the Reagan administration Jan. 7, be blocked because of continuing human rights violations in Guatemala.

Ernest, 27, of Golden, Colo., was arrested with a Spanish friend Jan. 11. The two have been accused of participating in guerrilla raids, but a State Department official stressed yesterday that no formal charges have been placed against them.

Ernest, who works for a family-owned oil company, rented a cottage in the picturesque western highlands of Guatemala with Maria Molenaar, a Spanish friend, The Associated Press reported from Guatemala. The region has been the scene of heavy fighting between leftist insurgents and the armed forces.

Under a state of siege declared July 1, people charged with participating in the insurgency are tried by the special tribunals whose membership is secret. A State Department official said the procedure probably was instituted to protect judges from guerrilla reprisals, but it has been strongly criticized by human rights groups.

The penalty for those convicted of "subversion" is death by firing squad. Four men were executed on Sept. 17 of last year.

Edmundo Vargas, secretary general of the Human Rights Commission, an agency of the Organization of American States, said he has sent a message to the Guatemalan government asking if due process was followed in the case and urging that the sentence be commuted