Former Italian premier Aldo Moro was secretively buried by his embittered family yesterday as the government, ignoring the family's wishes, scheduled a public funeral for the murdered political leader Saturday.

As the private funeral was being held, Italian Interior Minister Francesco Cossiga, the man who led the unsuccessful police efforts to find the kidnaped political figure during his 55 days of captivity, resigned from the Cabinet.

By his action, an unprecedented political act in Italy, Cossiga signaled a willingness to draw fire away from the rest of the minority Christian Democratic government.

As his resignation was being announced, the Moro family was holding a hastily arranged, unannounced funeral for the murdered leader in the village of Torrita Tiberina about 25 miles northeast of Rome, site of the family's country home. Moro's body had been found in the back of a car in downtown Rome Tuesday.

The secretiveness of the funeral arrangements was in accordance with the Moro family's bitter rejection of a state funeral by a government that Moro had accused in letters from captivity of having abandoned him.

Moro had explicitly requested that no representative of the state or of the Christian Democratic Party, to which he had devoted his political career of 30 years, be allowed to take part in his funeral.

A statement by Moro's family Tuesday said, "The family withdraws in silence and requests silence. History will judge the life and death of Aldo Moro." Yesterday, when the body was taken from the morgue, the family refused a police escort that was offered to them.

Ignoring the family's wishes, the government nevertheless scheduled a funeral mass for Saturday afternoon at Rome's huge Basilica of Saint John Lateran. Both houses of parliament held brief separate commemorative sessions yesterday. There were commemorative events at schools throughout the country in the morning, and flags on public buildings were flown at half-staff.

Amid the outpouring of public praise for Moro, Renator Curcio, on trial in Turin as the founder of the Red Brigades terrorist organization that took Moros life, expressed pride over his group's action.

"The killing, Curcio shouted in the courtroom, "was the highest possible act of hamanity in this class-ridden society." The judge expelled Curcio from the courtroom and had him charged with the additional crime of justifying a criminal act.

Before he left the courtroom Curcio warned that new terrorist atrocities could be expected. "Perhaps, you have not understood what has happened in this period and what is going to happen in Italy in the coming months," he told Judge Guido Barbero.

The first test of the political effect of the Moro kidnaping on Italian democracy will come Sunday in local elections affecting about 9 percent of the electorate throughout most of the country. ANLAYSTS BELIEVE THAT THE RESPECTIVE SHOWINGS OF THE Christian Democratic and Communist parties will be more of a reflection than usual of national trends rather than local issues.

This Sunday's elections are regarded as being psychologically important for the future of the Christian Democrats, who have suffered a series of electoral declines in recent years as the Communists have gained ground.

Some analysts speculate that the Christian Democrats could get a sympathy vote on Sunday and that revulsion against leftist terrorism may harm the Communists despite the pains they have taken to present themselves during the crisis as a responsible party of law and order.

The backlash against the terrorists includes growing demands for the restoration of the death penalty, abolished in Italy in 1943 after the overthrow of Fascist dictator Benito Mussolini.

The small neo-Fascist party is demanding the declaration of "a state of internal war against leftist terrorism."

The Communists, who are virtually partners in the government with the Christian Democrats, have been arguing privately against indiscriminate roundups of extreme leftists. The Communists express fear that arbitrary arrests could drive large numbers of leftist youth who are wavering on their commitment to the established state into the arms of the terrorists. The Red Brigades proclaim that they want to force the state to become more repressive to create a counterreaction they could exploit.

Nevertheless, most foreign and Italian commentators have been noting how unexpectedly well Italian democracy has resisted the onslaught of the leftist terrorists. "Italian society," said Italy's leading industrialist, Fiat automobile chairman Gianni Angelli, "has shown itself more strong and united than many had thought."

Many Italian commentators said yesterday that the only precedent in Italian history for the assassination of Moro was the murder by the Fascists of the popular and highly respected Italian Socialist leader Gaicomo Matteoti in 1926. That murder marked the death of prewar Italian democracy and the final phase of the Fascist takeover.

In Milan yesterday, an executive of the giant Montedison Chemical Co., Franco Giacomazzi, 50, was the third victim in a week in that city of a favorite terrorist tactic - crippling prominent men with gunshots in the legs. It was the 19th such shooting since Jan. 1.

Responsibility was claimed by a group called the Armed Popular Communist Front. The Red Brigades recently issued a public appeal for all the other clandestine leftist groups to join in an allout civil war againt the state.

There has been an undercurrent of criticism of the police failure to prevent the Moro kidnaping March 16 or to rescue him afterward. Yet, in his two year of dealing with the worst challenge to public order in recent Italian history, Cossiga won more respect from his own police than any other postwar interior minister, police officials say.

Premier Glulio Andreotti has not yet said whether he plans to accept Cossiga's resignation. Sources close to Cossiga intimated last night that he had decided soon after the Moro kidnaping that he would resign if the party leader did not come back alive.

As interior minister, Cossiga's resignation statement said, he accepted the "full moral and political responsibil - for the government's refusal to negotiate with the Red Brigades for Moro's release. He said it was the only course the government could follow and he called for "intensification of the fight against subversion."

There was immediate specualtion that Cossiga'w willingness to serve as a lightning rod for criticism probably involved recognition in advance by his Christian Democratic colleagues of a political debt.

Except for the insistence of the small Socialist and Radical parties that the government should have negotiated, most criticism has been muted until now. Some commentators, however, are beginning to say that the government made a major tactical blunder by foreclosing negotiations rather than playing for time in the hope of a tactical mistake by the Red Brigades.

Police say that in their hunt for clues they are taking Apart the red Renault automobile in which Moro's body was found. Its license plate was false, they said.

The Italian news agency quoted the autopsy report as saying that Moro was executed at about 6 or 7 a.m. Tuesday. The body was found in the car parked between Communist and Christian Democratic headquarters Tuesday at 1:30 p.m.