Pressure is on Israel's Labor Party.

Israel's Labor Party is pinning its hopes for forming a government on the ability of party leader Shimon Peres to reach agreement with the incumbent right-wing Likud bloc.

If Mr. Peres fails to pull together a ''national unity'' government, party analysts fear that Labor may be shut out of governments for the foreseeable future.

This worst-case scenario is painted by these analysts, who feel Labor's narrow victory over Likud last month was in some ways more profoundly disturbing for Labor than the party's defeats at the hands of Likud in 1977 and 1981.

The election showed a deep loyalty for the Likud both among Israel's Sephardic Jews - those from Arab and North African countries - and among youth. These groups voted for the party in large numbers despite its dismal economic record and failure to extricate Israeli troops from southern Lebanon.

One interpretation of the election, in which 75 percent of the nation's Sephardim voted for Likud while 75 percent of Israelis of East European heritage voted for Labor, is that Israel is moving steadily to the right. Members of both Likud and Labor agree with this assessment.

But perhaps more frightening for the left-leaning Labor is that, in the election, Labor had so antagonized the Sephardic Jews that they simply could not bring themselves to vote for Labor.

The election showed that ''no matter how bad a Likud government,... well over half of the electorate will find themselves constitutionally incapable of voting for the (Labor) alignment as it insists on presenting itself for the voters' approval,'' writes an analyst in the generally pro-Labor Jerusalem Post.

The party that ruled the Jewish state for three decades is increasingly seen by the Sephardims as elitist and out of step. Sephardic Jews have bitter memories of the discrimination they felt they suffered at the hands of the Labor Zionists when thousands of these Sephardim arrived here from Morocco, Yemen, and other Arab countries in the 1950s. For many Sephardim, Labor is irrevocably identified with the kibbutz movement that has become a symbol of oppression to some Sephardim.

''The Labor Party, it is the party of the kibbutzim,'' says Joseph, a Sephardic taxi driver and loyal Likud supporter.

''The kibbutzim do not work. We work. They are parasites.''

Conversely, former Prime Minister Menachem Begin and the Likud are seen by the Sephardim as trusted allies who do not look down on them because they are not from Eastern Europe.

''Begin had only three categories of people: them, the goyim (non-Jews); us, Jews; and me, himself,'' says a former Likud government member. ''For him, a Jew was a Jew, and the Sephardim loved him for it.''

It is that sort of deep-seated hostility that has some Labor Party members wondering whether they will find themselves permanently relegated to the opposition should Peres fail in his bid to form a government.

''If this country will have another four years of Likud government, Labor will be wiped out,'' says one gloomy Labor official.

The two parties have been unable, in seemingly endless rounds of talks, to reach agreement on key issues such as Jewish settlements on the West Bank and terms under which Israel would negotiate peace with Jordan.

The bad news for Labor is that even if Peres does end up leading a national unity government, such a solution may at best only postpone the decline of the party.

''We are attached to those demographic trends that are diminishing,'' observes David Twersky, a kibbutz member and editor of Labor's monthly magazine.

Party leaders acknowledge that Labor has been slow to change and seems unable to broaden its base of support, which comes from Jews of Eastern European background and from older Jews. But these leaders don't seem to have concrete ideas about how to reform.

One glaring difference between the two main parties has been the Likud's ability to recruit young members and facilitate their move up the party ladder. Labor fielded a list of parliamentary candidates who were almost all more than 40 years old. Among its top 40 candidates, Likud included more than 10 who were under 40.

''Before the election, I said the criticism that we were running only old people was ageism,'' Mr. Twersky says. ''Now I know that we really hurt ourselves by not putting young people on.''

It is impossible to tell which single factor cost Labor the most seats. It won 44 seats to Likud's 41, but Labor actually won fewer seats than it did in the 1981 elections. Likud also lost seats. Votes that had previously gone to the two largest parties went to more extreme parties on the right and the left.

Labor members interpret the results to mean that Israel may be becoming a nation of extremes. As Twersky puts it, ''The country is undergoing an incredibly profound transformation of its society.'' Even had Labor done better in the election, Twersky says, it would not have changed the fact that ''we ... have been a profoundly disturbed society.''

''What is Israel's soul?'' asks former Labor government spokesman Meron Medzini. ''We don't know. The election of 15 parties to the Knesset shows that we are not yet a nation.''

But Likud supporters say they welcome the change in Israel evidenced by the election results, and argue that unless Labor also changes, it will be unable to win back the confidence of the Israeli electorate.

''Today's Israel is different,'' says Ehud Olmert, Likud Knesset member and campaign strategist.

''Labor can't understand that, and this is exactly why they fail and will continue to fail. Without understanding, the Labor Party will never be able to recover.''

One criticism leveled at Labor by Likud supporters is that the party continues to equate a rejection of Labor with a rejection of the founding principles of Israel.

''The Labor Party says, 'This is my country and I'm ready to allow you to participate. The ethnic people of Israel say to them, 'This is the country of all of us,' '' Mr. Olmert says.

For Labor, regardless of how the government talks end up, the challenge will be to see if it still can find a common language with all of the country.

Mr. Medzini says: ''There are those in the party who say, 'Let's stay in the opposition and rebuild this party on ideological grounds.' ''