In the last month, television evangelist Jerry Falwell has broadcast a satellite television show from Jerusalem featuring Israeli Prime Minister Shimon Peres, denounced a proposal by Egypt's president that the Palestine Liberation Organization be included in a U.S.-sponsored peace initiative and apologized to a Miami gathering of rabbis for "excesses" by conservative Christians.

Falwell's activities present a paradox. He remains the nemesis of many American Jews, the point man of what they consider an intolerable right-wing threat to America's unique religious pluralism and a major reason that 71 percent of them voted for President Reagan's opponent last November.

To the chagrin of his U.S. critics, however, Falwell is received as an ex-officio ambassador of America's new Christian right by Israeli leaders who, despite pressure from some Jewish liberals, dare not turn away such a staunch supporter. At home, Falwell is making a major effort to mend fences with the Jewish community -- a political mission that some critics charge has a frightening theological motivation.

"I'm going to be their friend whether they want me to or not," Falwell said in an interview.

He remains bent on building a political coalition with conservative Catholics (on opposition to abortion) and with conservative Jews (on support for Israel), creating tension in the traditionally noncoalition-minded fundamentalist Christian movement.

Falwell told the conservative Rabbinical Assembly at their March 13 Miami session, "Twenty-five years ago many of us were saying this is a Christian republic . . . Now we say Judeo-Christian republic. There is a spirit of pluralism that did not exist then.

"We have had our excesses," Falwell said, "and we can only say we're sorry and we'll try and do better." He promised to "mobilize 70 million conservative Christians for Israel and against anti-Semitism."

Administration officials say that they are comfortable with his activities as an increasingly influential political ally and have made no effort to persuade him to lower his profile.

"If he wants to mend fences with the Jewish community, I'd encourage him to do that," said a White House aide. "It has no relation to our relationship with that community . . . . For a Republican, it's very, very good. We've been very supportive of Israel, and our opposition to affirmative action and quotas has been pretty popular."

While no one is betting that Falwell will win the Jewish vote for the Republicans in 1988, some Jewish leaders and other observers say that he is at least lowering the temperature of the debate.

Rabbi Marc Tanenbaum of the American Jewish Committee commented after the Miami session, in which he participated, "It was thrilling to watch Jerry Falwell become a born-again American."

Henry Siegman, executive director of the American Jewish Congress, was less sanguine. "I take Falwell at his word that he's a friend of Israel," he said, "and I don't believe he's an anti-Semite . . . . But he misses the point completely. It is not a tolerance for unorthodoxy that the American system is all about. It's that the government is not identified with any one group."

Other critics say that Falwell still is affiliated closely with Christian right leaders who continue to make insensitive statements about Jews and Catholics and have set up a "Christian talent bank" for government appointments.

Television producer Norman Lear, chairman of People for the American Way, a group he founded to combat Falwell's Moral Majority, called Falwell's Miami statement "a clear victory for those of us who have been fighting to protect the wall of separation between church and state."

However, he added, Falwell's organization has since mailed out at least one copy of writings in which he expresses sentiments for which he apologized.

Falwell said in a recent interview that he repudiates all such past material. "We have been careless with our rhetoric," he said, adding that he, unlike some other religious leaders, is willing to own up to various stands he has since renounced on such things as civil rights.

Jewish leaders say that Reagan's embrace of a "Christian nation" and his association with Christian leaders such as Falwell last summer thwarted the Jewish vote's accelerated movement toward the Republican Party that some had predicted in the wake of statements by Democratic candidate Jesse L. Jackson and one of his supporters, Nation of Islam leader Louis Farrakhan, that were called anti-Semitic.

Reagan's remark also helped spark an internal debate over whether American Jews can afford to be perceived as a single-issue community focusing on Israel's security and not on domestic issues such as those raised by the Christian right.

"I think Falwell's efforts will help lower the heat," said a Republican Jewish political activist familiar with administration thinking. "The 1984 presidential election was the first time the American Jewish community has voted on issues other than the state of Israel. The church-state issue is now close to being the No. 1 issue."

But the religious right's interest in the Jewish nation goes beyond political motives: Its militant pro-Israel foreign policy is tied directly to a belief, shared by many of its leaders, that Christ will come again in Israel, defeating the antichrist in the battle of Armageddon and saving only born-again Christians and a handful of Jews who would convert.

Critics are concerned that Falwell and others have linked this prophesy, called dispensational premillennialism, to nuclear technology in a way that makes nuclear holocaust seem inevitable and, for true believers, survivable. The doctrine became an issue in the 1984 campaign when Reagan made several references to Armageddon.

The "nuclearized" scenario includes the "rapture," in which Jesus will catch up bodily all born-again believers into the air; the invasion of Israel by Soviet, Arab and other armies; the destruction of Soviet communism in a nuclear war, and the return of Christ leading an army of the raptured Christians to fight the antichrist in the final battle of Armageddon in Israel. The Christians would be joined by surviving Jews who would convert to Christianity. Together they would form a "spiritual aristocracy" to administer the Millennium -- a 1,000-year era of peace under Christ in a purified world.

Though he supported it in earlier interviews and writings, particularly his "Nuclear War and the Second Coming," Falwell recently has made statements distancing himself from the nuclear interpretation.

Andrew Lang, an official of the Christic Institute, an interfaith public policy institute, says, "My basic position is that the support the new Christian right lavishes on Israel has certain ulterior motives . . . not understood in the Jewish community." The institute estimates that there are at least 8 million "nuclear dispensationalists" in the United States.

According to a top Israeli political observer, Falwell's "love story with Israel" started in 1977 when Menachem Begin came to power. "Falwell's people always asked for meetings with Begin, and they always got it," he said. "Begin did not mind. He felt that any friend of Israel was more than welcome," regardless of how some Jews felt about Falwell.

While the Israeli press featured "big pictures" of Falwell with top officials of Begin's Likud party, Peres has played down publicity within Israel about his relations with Falwell, the observer said. Peres' Labor party is "more sensitive about the feelings of the liberal Jewish community" than the Likud is, he said, "but as prime minister, Peres cannot afford the intellectual luxury of refusing to see Falwell . . . . Here we have a friend, whatever his motives."

Falwell's latest trip to Israel, his 15th, was part of a flurry of highly visible international activity.

In recent weeks he has debated the prime minister of New Zealand, which has refused port entry to U.S. nuclear-powered or -armed ships, at England's historic Oxford Union Club, on the morality of nuclear war; and he has announced a new operation to help feed the starving in East Africa using money raised through his "Old Time Gospel Hour" broadcasts.

While in Sudan to inspect the site of the operation and meet with Sudanese officials, he was invited to a state dinner given by the Sudanese president for Vice President Bush, whom Falwell has indicated he will support for the presidency in 1988. Bush was touring drought-stricken African nations. Representatives of both men say that the timing was coincidental.