President Carter ended two days of talks with Israeli Prime Minister Menahem Begin yesterday by predicting that Israelis and Arabs will go to a Geneva peace conference in October. But neither leader explained how the main roadblock can be overcome.

"I believe that we had laid the groundwork now, barring some unforeseen difficulty, that will lead to the Geneva conference in October. . We see [it] as being very likely," a confident Carter told reporters after saying goodbye to Begin at the White House.

Outlining his previously secret plan for peace talks at a crowded news conference several hours later, Begin ruled out any role for the Palestine Liberation Organization or any of its members at the Geneva meeting. The presence of any known member of the PLO in another Arab delegation - a device often suggested to resolve the procedural impasse - "means PLO participation and . . . we cannot negotiate with the PLO," Begin said.

There was no public indication that the Arab nations are prepared to abandon their demand for PLO participation at Geneva, and American officials could cite no private indications that the Arabs are ready to do so.

Foreign Minister Ismail Fahmi of Egypt, the Arab government most anxious for a Geneva meeting, was quoted by the Cairo newspaper Al-Ahram in yesterday's edition as calling the PLO "the sole legitimate representative of the Palestine people" and is insisting on PLO participation as the first principle of Egypt's drive for a Middle East settlement.

Cairo Radio said that Begin plan, as reported by Israeli news media, "is rejected in form and substance." Saudi Arabian newspapers called the reported plan a prelude to a return to war. A PLO spokesman in Beirut said "the PLO rejects the Begin plan from A to Z, because it negates the right of the Palestinian people to self-determination and nationhood."

As forecast, Begin limited his public disclosure to the procedural aspects of his plan and refused to say how much withdrawal from occupied territory he is contemplating. News reports from Jerusalem, which have not been contradicted, said Begin has in mind extensive withdrawals from the Sinai and some withdrawal from the Golan Heights but continuing Israeli control of the occupied west bank of the Jordan River.

To give up the West Bank to a "so-called Palestinian state," Begin told reporters, would bring every Israeli citizen within the range of Soviet-made artillery and permit a tank column to bisect Israel in 10 or 15 minutes across its narrowest point only nine miles from the sea. "This would be a mortal danger . . . the end of our statehood, independence and liberty," he said.

Saying that "no prior commitments" to the shape of a peace agreement can be asked or given by either side before sitting down to bargain, Begin proposed the following procedures:

A Geneva conference which meets and quickly divides itself into three or four "mixed commissions," each of which pits Israeli negotiators against a team from one of its neighbors - Egypt, Syria and Jordan, and Lebanon if it wishes to take part.

Bilateral commissions of Israel and its neighbors outside the Geneva context, under the good offices of the United States, if a Geneva meeting is not possible.

"Proxmity talks" in which the United States acts as a mediator between Israel and its neighbors in indirect discussions, if all else fails.#TWhile Begin's public "plan" did not indicate any change on the Palestinian representation issue and gave no hint of territorial concessions on the West Bank, American officials appeared to be greatly relieved that it did not renounce the concept of a comprehensive settlement and thus lead to an open U.S.-Israeli confrontation at this early stage of bargaining.

Senior U.S. officials professed to see progress on procedures and a little more flexibility in substance during the Begin talks. They expressed hope that Secretary of State Cyrus R. Vance will be able to build on this to obtain agreement to a Geneva conference during his Mideast trip now scheduled to begin Aug. 1

Carter and Begin praised each other in warm terms in speaking to reporters yesterday, and were said to have established personal rapport in the past two days. Begin said there was no U.S. "pressure" on him and no "confrontation."

Carter said he did not seek to resolve the "strong" substantive differences on territory and the Palestinian question during his talks with Begin, saying the positions of the Arab and Israeli leaders at a Geneva conference are best left to them.

"I will stick to my public views [about the conditions for a peace agreement] but I think now is the time to be quiet about the specifics," Carter said. He said this silence is strongly desired by Begin and, he believes, by the Arab leaders as well.