Israel's fragile government of national unity entered a new phase today following union elections that gave a clear boost to the Labor Party half of the government that is headed by Prime Minister Shimon Peres.

In final returns from balloting yesterday, the Labor Party won almost 67 percent of the vote to select representatives to the governing conference of the Histadrut, Israel's union federation, to which about 85 percent of the country's work force belongs.

The Likud bloc headed by Foreign Minister Yitzhak Shamir, which shares power with the Labor Party in the national-unity government, won 21 percent of the vote in the union contest.

Labor also won control of all but one of the 72 local labor councils in Israel.

The Labor Party was never in danger of losing its solid majority control of the Histadrut, which it has enjoyed since the union federation was founded in 1920 by the early Labor Zionists, who later oversaw the creation of the state of Israel in 1948. However, the vote was the strongest showing by Labor in the last five Histadrut elections, which are held every four years, and was seen by some as an indication that the party has finally reversed the decline it suffered during much of the 1970s and early 1980s.

Moreover, it has been widely assumed here that Peres and other Labor Party leaders have deliberately played down their differences with the Likud bloc in the government to prevent an open rupture that could affect the Histadrut elections. A senior Labor Party official predicted before yesterday's voting that Peres would immediately begin pressing the Cabinet to impose more stringent economic austerity measures.

While yesterday's union election outcome was encouraging to the Labor Party, Hanoch Smith, a leading Israeli pollster and political analyst, said his polls confirm the findings of Labor officials that the party has not made significant gains on the national level since last summer's parliamentary elections, which ended in a virtual deadlock between Labor and Likud and their small party allies, forcing formation of the national-unity government.

He said there has been "a revolutionary change in the public attitude toward Peres," who continues to rise in the polls, but that party identification remains strong in Israel and that Peres' new personal popularity has not been transformed so far into major gains for his party.

With union elections over and the Labor Party's control of Histadrut solidified, Peres was seen by analysts as enjoying increased freedom of action in domestic and foreign policy, including the possibility of forcing a breakup of the unity government and parliamentary elections before he is due to turn over the post of prime minister to Shamir in September 1986.

Peres appeared to signal a tougher, post-Histadrut elections attitude during an appearance before the parliament's Finance Committee today. Israeli radio quoted him as saying he would resign if the parliament did not quickly enact a series of economic measures that have been approved by the Cabinet.

Smith said in an interview today that while Labor's gain in the Histadrut, from 62 percent in 1981 to almost 67 percent yesterday, represented "no great shift," it could have important psychological ramifications in Israeli politics.

"It will probably lead them to entertain ideas about early Knesset parliamentary elections," Smith said. "They can now allow themselves the luxury of thinking in those terms. They may not feel they have to make so many concessions to the Likud to keep the national-unity government together."

While clearly pleased by the outcome of the union elections, Labor Party officials were cautious in interpreting the results.

"It's encouraging, but I hope it doesn't lead to any stupid mistakes, like thinking this can be translated into national elections," said Israel Peleg, director of the government press office and a senior Labor Party political strategist.

The Histadrut is the foundation on which the Labor Party stands and through which it dominated Israel's politics from 1948 until 1977, when the Likud bloc first captured control of the national government. It is a vast economic empire and also, through affiliated business and industrial concerns, the country's largest employer.