Israel's Labor alignment, defeated in the country's general election last month, apparently retained its hold over Israel's second most important power base, the federation of labor unions known as Histadrut, in elections today.

The vote, which involved about 1.4 million Israeli workers, is seen here as the first setback to the new Israeli government, which was sworn early this morning.

It is also considered an indication that much of the Isaeli electorate may have had second thoughts about its swing to the right in the May 17 parliamentary election. The outcome is expected to give new hope to the Labor opposition in Parliament, which may now intensity its attempts to bring down Prime Minister Menachem Begin's narrowly based conservative government.

Early projections complied by Israeli television indicate that in today's elections to the Histadrut governing bodies, the Labor alignment has suffered only a slight setback and will maintain its majority, while Begin's rightist Likud Party, which hoped to repeat today its parliamentary upset of last month, gained only slightly.

In the 1973 Histadrut election, the Labor alignment had a 58 per cent majority as against only 22 for Likud affiliates. Israeli television projections this evening gave the Labor alignment about 55 per cent of the vote, Likud about 27.5 per cent and 9 per cent for the new center party, the Democratic Movement for Change, which participated in the Histadrut election for the first time.

The centrist Democratic Movement, headed by Yigael Yadin, did better in the Histadrut election than most experts predicted, especially since this party draws about 50 per cent of its ranks in Parliament from voters who are not Histadrut members. The Movement had hoped, however, that the Labor alignment would not be able to retain its control over the Histadrut without Movement support.

More than 58 per cent of Israel's adult population, and 80 per cent of the salaried workers, are members of the Histadrut. Formed 57 years ago, it is much more than a super union with a decisive influence on the country's price and wage policies. It is also the owner of some of Israel's largest industries and agricultural units.

At least 25 per cent of Israel's gross national product is produced by Histadrut-owned enterprises. It also controls a vast infrastucture of health, welfare and cultural services.

Although there have been clashes in the past between the government and the Histadrut over wage policies, the fact that the leaders of both groups belonged to the same party enabled them in most cases to reach a consensus. Some observers fear that an open confrontation between the Histadrut and the Likud government could disrupt labor relations at a time when Israel need tranquility on the labor front.

Former Prime Minister Golda Meir, who was among the jubilant crowd that assembled at Labor Party headquarters in Tel Aviv tonight, said in reply to a question: "The Labor alignment fought the Histadrut election with a platform that does not coincide with the program of the Likud government. We shall do our utmost to implement our program."