The Rev. Jesse Jackson today said Palestine Liberation Organization positions indicated a "recognition of sorts" of Israel's right to exist and that President Carter had a "moral obligation" to talk to PLO chief Yasser Arafat.

The black American civil rights leader, who arrived here Friday at the head of a 17-member delegation of ministers, members of his PUSH (People United to Save Humanity) organization and journalists, said he stressed during meetings with Arafat that the PLO must reassess its policy toward Israel and "break the cycle of terror and pain" in the Middle East.

At one of the meetings, Arafat, in reply to a question, expressed a desire to meet with President Carter.

Jackson later flew to Cairo to confer with President Anwar Sadat, continuing his unofficial Middle East fact-finding mission. On arrival in Cairo, Jackson said the PLO does not seek to "exterminate Jews."

Jackson said in Beirut that the Palestinians had accepted Israel by saying their own state could be established on parts of former Palestine within boundaries that will be negotiable.

Present at meetings with Arafat in his home in the Palestinian-dominated Sabra quarter of West Beirut were various members of the PLO executive committee. Jackson's delegation had dinner at the guerrilla leader's house.

Jackson said there is "flexibility" among the PLO executive committee members. He asked them to prepare a document to be given to him Wednesday, after he meets with Syrian President Hafez Assad in Syria. Jackson said they should clearly state in the document "where they are" and stress their aspirations rather than what they oppose.

Jackson said the Palestinians are willing to negotiate for a state on the West Bank and the Gaza Strip and that they expected an "international committee" to deal with the geographical details of the plan.

The black leader said the PLO was also willing to accept the United States as the main bargaining force in the process. Jackson said Arafat "actually desires to meet with Carter to explain to him his point of view."

During a two-hour meeting in Arafat's living room, the PLO chief responded with alacrity when asked by a journalist whether he would meet with the U.S. president.

"Please, if you find a way, I will accept. Why are they refusing to talk to us?" Arafat said, throwing his arms up in the air.

He asserted, "We believe dialogue is very important."

He said he was told by his Palestinian hosts that their interpretation of the Palestinian National Charter must be heard instead of the perceived interpretation of others.

"They [the Palestinians] contend that the idea of driving Israelis into the sea is militarily unthinkable, impractical and immoral," Jackson said.

However, their point is that "until there is some kind of concrete evidence that the occupation will cease, that even under international law they have the right to armed resistance and that there is some correlation between the armed resistance and their feeling of hopelessness and of being ignored," he added.

"Asking them simply to denounce armed resistance is to humiliate them and neither side should be subject to humiliation in this transition from war to peace," Jackson said.

He said the PLO executive committee's legal explanation for not recognizing Israel now is that "only a state can recognize another state."

Jackson said that Carter should accept the overture made to him by Arafat. Jackson said Carter has "a real moral obligation" to meet with the PLO leader.

Although he met with Carter before setting out on his Middle East tour, which has so far taken him to Jordan, Israel and Lebanon, Jackson said the U.S. president did not give him any special message to Arafat but told him his visits to Arab capitals were very "important."

Jackson said he would meet with Secretary of State Cyrus Vance, Carter and U.S. special envoy Robert Strauss upon his return.

Jackson's Middle East tour has raised objections by some Israeli officials that he and other U.S. black leaders are meddling in sensitive Middle East peace negotiations. U.S. black interest in the Palestinian question was aroused when U.N. Ambassador Andrew Young resigned following an unauthorized meeting with a PLO official.

[Meanwhile, a bomb blast today stopped trains between Tel Aviv and Jerusalem as Israeli security forces went on alert for guerrilla attacks during Israel's holiest day, Reuter reported from Jerusalem.]