El Salvador's Catholic Church has urged a reinvestigation of the 1980 murder of Archbishop Oscar Arnulfo Romero.
Archbishop Romero was shot dead as he performed mass
The call follows a US court ruling that a man accused of conspiring to murder the archbishop should pay $10m to one of the clergyman's relatives.
But Salvadoran President Antonio Saca has said relaunching the investigation would only open the wounds of the past.
The killing of Oscar Romero, by a sniper as he held Mass, helped plunge the country into a 12-year civil war.
His death has gone unpunished mainly because of a Salvadoran amnesty law.
Last week, a court in California held the first hearing in connection with the murder, and defined it as a crime against humanity.
It heard evidence against retired Salvadoran army officer Alvaro Rafael Saravia, who has lived in the US for the past 20 years.
Mr Saravia was said to have been a close associate of the man who masterminded the killing, and was accused of providing money and logistical help in the assassination.
He had not been seen in public since the civil lawsuit was filed against him last September, and the hearing was held in his absence.
The Roman Catholic Church in El Salvador said the court's ruling showed the government was required under international law to find those responsible for the killing, despite the amnesty.
"The amnesty law cannot be applied to cases of crimes against humanity, in cases of grave violations of human rights," said Maria Julia Hernandez, of the San Salvador Archdiocese.
"The case of Monsignor Romero is a paradigmatic case of impunity. It is a crime against humanity."
But President Saca said that, while he regretted events brought about by the war, he had been elected to deal with El Salvador's future, not its past.
"I believe opening the wounds of the past would not be the best thing for a country that's moving towards the future," he said.
A truth commission set up by the United Nations in the 1990s concluded that the plot to kill Archbishop Romero was led by the former army major, Roberto d'Aubuisson.
Mr d'Aubuisson, who died in 1992, was accused of running right-wing death squads in El Salvador during that country's civil war in the 1980s.