The Italian Communist Party and Italy's ruling Christian Democrats both suffered minor losses in two-day regional elections yesterday and today that left the balance of power between them basically unchanged. The results, nevertheless, seemed likely to strengthen Premier Francesco Cossiga's two-month-old, three-party government.

Almost complete results from elections in 15 Italy's 20 regions gave the Christian Democrats 36.6 percent, the Communists 32 percent and the third-ranking Socialists 12.5 percent. There were also key contests in more than a dozen leftist-run cities but those results were not expected to be known before Tuesday.

Only 88.5 percent of Italy's 42.5 millin eligible voters went to the polls, compared to 91.5 percent in 1975 and 90.4 percent last year. The drop in the turnout, the lowest since 1946, is thought to reflect growing political disaffection.

The elections to regional, provincial and municipal governments represented the first electoral test since a national vote last June in which the Communists suffered significant losses compared to an unprecedented high of 34.5 percent polled three years before.

The setback for the Communists continued a two-year slump for the West's most powerful Marxist party and seemed likely to furter slow the Communists' flagging drive for a role in a national government.

The results, down 1.7 percentage points from the Communists' share of the vote in the last regional elections, do not necessarily mean that the Communists will lose control over any of the six regions they now run together with the Socialists.

The Communists' losses came in the south where they control several major cities, like Naples, but no regions. They made slight gains in northern and central Italy.

The Christian Democrats lost 1.5 percentage points in comparison with last year's elections and made only minor gains compared with 1975.

But the Communists' failure to increase their share of the vote -- together with a strong showing by the Christian Democrats' Socialists and Republican allies -- signified a boost for Cossiga's government, the first in six years with parliamentary majority.

There were no parliamentary seats at stake in the elections called to choose 15 regional, 86 provincial and 6,579 municipal governments, including those of most of Italy's major cities, with the exception of Rome.

But rather than treat the election primarily as a test for their "new way of governing" in leftist-controlled cities like Turin, Milan, Naples, Venice and Florence, the Communist campaign focused on accusations of government inefficiency.

Communist Party leader Enrico Berlinguer, who said tonight that his party would continue its policy of vigorous opposition, had termed the Cossiga government "dangerous," alleging that it has failed to deal effectively with inflation, terrorism and international affairs.

The campaign became particularly bitter toward the end when the Communists decided to give essential backing to a move to begin proceedings to remove Cossiga. The premier, a former interior minister, has been accused by a confessed subversive of protecting the terrorist son of a fellow Christian Democrat from arrest.

Because of this, terrorism became a major campaign issue here. This was ironic because substantial inroads have been made against leftist terrorism recently and because the Communists have been a major source of support for the government's tougher antiterrorist measures.

Although they did not focus their campaign on the cities under their control, the Communists have been fearful of losing control -- and with it considerable prestige -- in major centers such as Naples and industrial Turin.

Communist leaders in Rome said today they expect to maintain their lead in those cities but no significant results were yet available.

The big winners in this weekend's elections were the Socialists, who had been divided over party leader. Bettino Craxi's decision to return to a center-left alliance with Christian Democrats.

The party's gains in relations to both 1975 (0.6 percentage points) and 1979 (2.6 percentage points) are thought likely to strengthen Craxi and, indirectly, Cossiga. The Social Democrats, the Liberals and Neofascists also improved their showing compared with last year.

Socialist gains are thought in part to reflect support from the 3.5 percent of Italians who last year supported the small but vocal Radical Party. The radicals ran no candidates this year and urged followers to abstain or ruin their ballots.