A statement attributed to Red Brigades terrorist announced yesterday that former premier Aldo Moro, one of Italy's leading political figures, was executed by his leftist kidnapers and his body dumped into a mountain lake northeast of Rome.

A massive search of the lake by police, soldiers, firemen and skindivers failed to produce the body of the 61-year-old president of the ruling Christian Democratic Party. A Red Brigades statement Saturday said Moro was sentenced to death by a "people's trial."

The announcement, which sent shock waves through Rome yesterday, promised more executions, specifically mentioning Premier Giulio Andreotti and two senior Christian Democratic politicians.

Let them, it said, "and all those who support the regime start shaking for their misdeeds."

The Red Brigades statement, the authenticity of which could not be ascertained, warned that "this is only the start of a long series of suicides."

The reference that Moro's "execution" was "by suicide" was apparently a mocking reference to the controversial death of several members of the Baader-Meinhoff gang in West German prisons. The Red Brigades, who kidnaped Moro in a street ambush March 16, are ideologically akin to the West German terrorist group.

Throughout the day, Italian television broadcast continuous news about the case as hundreds of police and troops converged on Lake Duchess, at an altitude of 6,000 feet on Mt. Velino. The small volcanic lake, which is about 100 yards wide and less than one quarter mile long, lies in an isolated, snowbound area about 60 miles northeast of here.

The banks of the lake were packed with snowdrifts up to 12 feet high and its surface covered with ice. Police said there were no signs of recent activity in the area. Nevertheless, the search was to resume at daybreak today.

The failure to find any trace of Moro raised the possibility that the Red Brigades communique yesterday may have been a hoax designed to divert the searchers. The ruling Christian Democratic party issued a statement saying Moro's fate is "absolute uncertainty" and that there is a "thin ray of hope" that he was alive.

The communique, the terrorists' seventh since Moro was kidnaped in a bloody street attack in which his five bodyguards died, was quite specific about the place where the politician's corpse could be found.

It said, furthermore, that yesterday - the anniversary of the first post-World War II elections which gave the Christian Democrats a major victory over the Italian left - marked the end of 30 years of Christian Democratic "dictatorship."

A last ditch appeal to the terrorists' "humanitarianism" was made Monday by the Christian Democratic Party, the Vatican, some leading Italian Socialists, and several international bodies including Amnesty International, "Caritas" and the Red Cross.

Political and intelligence sources here appear convinced that in recent days something must have happened to convince the Red Brigades to cut short Moro's "trial" and to announce his death. They speculate that Moro may have died accidentally, that internal disagreements among the terrorists may have provoked an unexpected policy change, or that the Red Brigades feared police were closing in.

Flooding in an apartment on the outskirts of Rome, yesterday led police to their first major breakthrough in the Moro case - the discovery of what could have been the group's major hideout. Firemen called to investigate water leaking from an apartment in an outlying residential area, discovered an arms cache, false foreign and Italian license of a Red Brigades messages, and several airline uniforms which might have been those worn by four of the kidnapers on March 16.

After questioning the neighbors and searching the apartment, police put out an all points bulletin on its occupants and several other persons whose photographs were found there.

Some Italian politicians, however, continue to believe that the Red Brigades last two messages - Saturday's regarding the conclusion of the trial, and yesterday's regarding the execution - may be part of an attempt by the terrorists to raise the tension level here in order to force government and political authorities into negotiations.

The Italian Democratic government and the Communist Party, the second largest party in the country, have maintained a hard-line, "no deal" position from the start. Some Christian Democrats, as well as Moro's family and friends, are known instead to have favored bargaining attempts designed to spare the life of a man who had been expected to become Italy's next president.

Still others think yesterday's message, shorter than usual and "delivered" only in Rome instead of in the usual four Italian cities, may be a hoax. Intelligence experts here said they had "no reason to doubt the message's authenticity," but a detailed examination of the photocopied document has still not been completed.

Top-level Christian Democrats and Communists waited anxiously yesterday at their respective party head-quarters here for news of Moro's fate. According to one high-level Communist, the Red Brigades major goal appears to be that of demoralizing and dividing the ruling Christian Democratic party, and thus the country.

He said that the Communists, whose current official role in the government majority was worked out by Moro shortly before his kidnaping, would give the Christian Democrats full support in their moment of travail.

Yet another theory is that the Red Brigades "staged" both the Lake Duchess search and the discovery of the hide-out in an attempt to divert the attention of the police while they carried out an as yet unknown move in another direction.

The Communist position was demonstrated yesterday afternoon when party secretary Enrico Berlinguer made a highly unusual and apparently unprecedented visit to Christian Democratic headquarters where he offered his sympathy and moral support.