A new religious-political alliance took a tentative step forward here this week as Jews and Fundamentalist Evangelical Christians--two groups that have viewed each other with fear and suspicion for decades--met in a series of private and public sessions.

Fundamentalists traditionally have mistrusted Jews and have approached them only to convert them to Christianity. Jews feared the Fundamentalists' evangelistic fervor, often directed at young jews on college campuses by such groups as Jews for Jesus. The emergence of Fundamentalist Christianity into the political arena two years ago further heightened Jewish fears of a resurgence in anti-Semitism.

Recent developments, however, have been in sharpest contrast to the old mutual dread. Jewish and Fundamentalist leaders sat down together here this week to talk; charismatic Christian fundamentalists joined members of the city's largest Reform synagogue last night for Sabbath services and next week Israeli Prime Minister Menachem Begin is scheduled to appear on the Christian Broadcasting Network's 700 Club. In addition, he will keynote a rally in support of Israel on Tuesday in the very heart of Fundamentalist Christendom: the First Baptist Church in Dallas.

What has brought these two previously hostile groups together, they say, is their mutual concern for Israel.

Fundamentalist evangelicals view creation of modern-day Israel as "an undeniable fulfillment of Biblical prophecy, the herald of the coming Messiah," according to an eight-point statement of support that is being circulated by the California-based evangelical group known as TAV, which takes its name from the last letter of the Hebrew alphabet. TAV initiated the Jewish-Christian encounters in Washington this week.

Increasingly, these Fundamentalist Christians who take the Bible literally translate prophecies about Biblical Israel into political support for the state of Israel.

At a news conference at the outset of the Jewish-Fundamentalist Christian dialogue on Thursday, Ed McAteer, president of the politically conservative Round Table, linked American well-being to the nation's faithfulness in heeding what he interpreted as Biblical commands to aid and support Israel.

"Our land continues to be first" because of three things, McAteer told the press: "because of the prayers of God's people;" because American Christians "supply 65 percent" of the missionaries working to convert the rest of the world to Christ, and "because we have obeyed God's word" in supporting Israel.

Rabbi Joshua Haberman, head of the Washington Hebrew Congregation where the Jews and Christians joined in a "Sabbath of Solidarity With Israel" last night, spoke on Thursday of the encounter as "opening our doors," but he warned against expecting too much of the dialogue. The two groups, he said, would "not agree on every point," but, "there is no need to disagree on every point."

Spokesmen for both sides were unanimous in their claims on Thursday that Israel has been unfairly judged in the media and elsewhere for its conduct in this summer's fighting in Lebanon. "We should not ask Israel to conduct its foreign policy on the level of the angels while still dealing with human beings," Haberman said to the group's enthusiastic applause.

Haberman, in a communication to members of his congregation, responded more to reservations that many Jews have about cooperation with evangelical Christians. Writing in the congregational news bulletin, the rabbi said " . . . it is as erroneous to lump them all together under one political column as it is to charge Jews with voting as a block. For every one Evangelical follower of the Rev. Jerry Falwell's politics, there are at least 10 who march to the sound of a different drummer."

Dr. Albert Hornblass, an ophthalmologist who is president of the Jewish Board of Education in New York City, said he participated in the dialogue "because I feel the state of Israel needs friends . . . We have had a sense of isolation, a sense of 'where are our friends?' "

"If we'd had this dialogue in Germany, Nazism would never have arisen," said Rabbi David Z. Ben-Ami, president of the American Forum for Jewish-Christian Cooperation.

Douglas Shearer, president of TAV, underlined the political determination of his group. "We are going to undertake a campaign" aimed at stopping "the shift in American policy away from support of Israel," he said.

TAV's eight-point declaration begins with a commitment "to the security of Israel. We believe that ALL of the Holy Land is the inalienable possession of the Jewish People: that the promises made to Abraham, Isaac, and Jacob have never been abrogated . . . . " This view -- that present-day Israel should extend to the boundaries of the Biblical state -- is shared by Begin but not by many Jews, here or in Israel.

The statement declares Jerusalem "the eternal and indivisible capital of the Jewish State and should not be internationalized or made the subject of any negotiation or compromise."

It also declares that Israel "should not be required to cede disputed land in return for 'peace.' " It denounces anti-Zionism and anti-Semitism and affirms "that Jews everywhere remain the 'Chosen People of God' and that God blesses those who bless them."

Rabbi Herzel Kranz, of the Orthodox Silver Spring Jewish Center, where the Fundamentalist Christians and Orthodox Jews gathered for a rally Thursday night, translated the campaign into contemporary political idiom. "We're looking for signatures," he said, "in order to send a message to the president . . . . We're here to make sure he stays the course."