The Rev. Jesse Jackson, ignored by Prime Minister Menachem Begin and other Israeli leaders, began a three-day peace-seeking visit here today with a thinly veiled threat that black Americans could attempt to influence continued U.S. support of Israel if the Palestine Liberation Organization remains excluded from peace negotiations.

While repeatedly stressing that Israel can trust the United States and that black Americans will defend the Jewish state's right to exist, Jackson warned that blacks represent a "political reality that Israel should not ignore.

"We do have 17 congressmen. We do have 15 million eligible voters. We are the difference in presidential elections," Jackson declared at a press conference at Ben Gurion International Airport.

Pointedly noting that Israel receives more U.S. aid than "the whole African continent," Jackson said, "I would hope that Mr. Begin's rejection of us does not indicate that he rejects that which we have to offer. We have tax money to offer, we have votes to offer, we have moral support to offer," Jackson said.

Then, he added, "We tend to support people who support us."

Jackson, head of Operation PUSH (People United to Save Humanity), became the object of a growing controversy in Israel when Begin, acting on the advise of Foreign Minister Moshe Dayan, refused to meet with the black leader because of his support of the PLO and because of statements the prime minister said "bordered on anti-Semitism."

Similarly, Begin refused to meet with another black delegation led by the Rev. Joseph Lowery, president of the Southern Christian Leadership Conference, and D.C. Del. Walter Fauntroy.

After visiting PLO chief Yasser Arafat in Beirut, the SCLC group returned to the United States yesterday without visiting Israel as originally planned.

Originally, Israel's Foreign Ministry had planned to refuse Jackson and his delegation of religious leaders the normal logistical assistance offered to groups visiting Israel. But it reversed itself last night and said that its official visitors department would help with scheduling, transportation and other arrangements.

Despite Begin's refusal to receive the group, Jerusalem Mayor Teddy Kollek and opposition Labor Party leader Shimon Peres agreed to meet Jackson, who also said he plans to visit West Bank Palestinians and tour the Christian militia-held southern Lebanon enclave.

Peres, who will see Jackson Tuesday, was quoted as saying, "we have already met with persons who hold views like his and tried to win them over, and there's no point in not meeting with them now, particularly against the backdrop of the exacerbation of Jewish-black relations in the United States.

In his airport press conference and again in tonight's meeting with Kollek and a group of Christian and Moslem residents of Jerusalem, Jackson stressed that wherever the United States has a national interest, black Americans also have an interest.

He said the United States has not only a moral commitment to Israel's defense, but an "economic interest" amounting to $5 million a day and a geopolitical interest in the entire region.

"We want to be heard as blacks become more assertive of foreign policy. We reserve the right to challenge a given position." Jackson said. But, he said, "disagreement must not be seen as tantamount to anti-Semitism."

Jackson said he regards the PLO as the "legitimate bargaining agent" of the Palestinian people, and that the time had come for Israel to relieve the United States of its 1974 Sinai disengagement pledge not to negotiate with the PLO.

"I resent being bound by a gag rule. Israel must trust America. Israel must take the initiative and relieve America of our gag policy, our no-talk policy that renders America unable to protect our own interest in the Middle East," Jackson said. His comments were a reference to the U.S. policy of not talking to the PLO.

When Kellek raised the issue of terrorism during what amounted to a town meeting at Jerusalem's municipal hall, Jackson appeared sympathetic, saying, "We understand the cycle of terror, the cycle of pain;

"Terrorist tactics and nonrecognition of Israel are the only two things that stand between them (the PLO) and independence," Jackson said, indicating that he believed Arafat is ready to recognize Israel but is not ready to say so.

He added that "115 nations of the world recognize them (the PLO). That's too many nations to ignore. Now that they are center stage, they must recognize Israel."

When Kollek suggested Jackson should visit some of the hospitalized victims of Thursday's terrorist bomb blast in central Jerusalem, Jackson immediately replied, "I do want to visit some people maimed by terror and maybe visit some graves." His aides and city officials immediately began confering on details of a visit to Hadassah Hospital, where some of the 51 victims are being treated.

Israeli sources said that Begin's decision not to meet Jackson was heavily influenced by Dayan, who argued that the black leader's public statements following the resignation of U.N; Ambassador Andrew Young bordered on anti-Semitism and were an affront to Israel;

Moreover, Dyan is known to have argued that since Jackson has presented himself as a potential mediator between Israel and the PLO, a Begin-Jackson meeting could upset the delicate Egyptian-Israeli negotiations on autonomy for the West Bank and Gaza Strip Palestinians.

Foreign Ministry sources said Dayan, who remained in the United States following the Sinai peacekeeping negotiations conducted at the State Department, presented his views to Begin in telephone calls and by cable.

Begin's closest advisers said they were particularly incensed by statements attributed to Jackson to the effect that Begin is a "terrorist" and that Israel is a "state of oppressors."

They acknowledged that the black leader appeared to modify his stand in recent statements, including a filmed interview on Israeli television in which Jackson said he had meant that Begin had once been a terrorist but became a statesman. The same phenomenon could occur to others labeled terrorists today, Jackson said.

Following his stay here, Jackson is scheduled to visit Ammah, Damascus and Beirut, where he will meet Arafat. Jackson said he also plans to meet Egyptian President Anwar Sadat in Cairo.