President Carter's talks with Israeli Prime Minister Menachem Begin ended yesterday with the United States, Israel and Egypt in agreement on negotiating device that they hope will enable them to meet the May 26 target date for an accord on Palestinian self-rule.

Although Begin alluded to this device at a press conference, its details were not spelled out publicly. However, informed sources said it involves interpreting the 1978 Camp David accords in a way that would permit establishment of a self-governing authority for Israeli-occupied Arab territories even if full agreement has not been reached on the authority's powers.

The descriptions given by the sources seem to imply that elections for a self-governing authority could take place and its members could be installed in office even though Israel and Egypt disagreed on such questions as the extent of its police powers or its authority over land usage.

In that case, some mutually-agreed-on Egyptian-Israeli entity presumably would retain control of these functions until the disagreements have been resolved. At that point, these powers would be transferred to the self-governing authority.

The sources said this scheme, together with an announcement by Carter and Begin of plans for intensified negotiations, could significantly enhance the chances of a breakthrough in the drive to grant some measure of autonomy to the 1.2 million Palestinian inhabitants of the West Bank and Gaza Strip.

Carter, appearing before reporters following the conclusion of the talks, said only that the United States and Egypt had agreed to Begin's proposal for marathon, continuous negotiations in Israel and Egypt during the 40 days remaining before May 26.

However, the sources said, potentially the most important thing to emerge from Carter's discussions with Begin, and with Egyptian President Anwar Sadat last week, was agreement on using a device described in the Camp David accords as "a continuing committee" as a means of setting aside for the time being any issues left unresolved in the upcoming burst of negotiations.

The Camp David agreements are the basis for the attempt to create a self-governing authority in the occupied lands for a five-year interim period. One of the Camp David provisions specifies that, during this period, Egypt, Israel and Jordan, if it decides to join the process, will "constitute a continuing committee" to deal with the problems of Palestinian refugees who left these areas after they came under Israeli control in 1967.

However, the article in the Camp David accords describing this function also adds: "Other matters of common concern may also be dealt with by this committee."

According to the sources, Begin and Sadat have agreed to interpret that language as meaning that a self-governing authority can be created even if its powers and responsibilities have not been fully defined. Instead, the unresolved issues will be referred to "the continuing committee" for further negotiation, while the self-governing authority goes into limited operation and exercises those powers that had been agreed upon.

The sources conceded that using this legalistic device could result, at least in the short run, in a mechanism that is only the skeleton of a governmental body -- one lacking many of the specific powers necessary to give it form and substance.

That, the sources also admitted, could make even more difficult the potentially formidable problem of getting the already suspicious Palestinians to cooperate with the self-governing authority and gaining recognition for it elsewhere in the Arab world.

But, the sources contended, the scheme, for all its drawbacks, offers an opportunity to keep the Mideast process moving forward by making it possible to put some kind of self-governing system in place. Otherwise, the sources noted, a prolonged failure to agree on all the powers to be vested in the self-governing authority would push its creation further and further into the future and increase the danger of the U.S.-mediated peace process ending in failure.

The importance with which the three governments involved in the autonomy talks view this device was hinted at by Begin at his press conference yesterday.Asked whether the talks here had led to new instructions for the negotiators, he replied: "We have accepted certain formulations about the continuing committee."

He declined to be more specific, responding to questions about the "continuing committee" by saying its main job would be to deal with refugee questions and contending that the major autonomy issues should be worked out in the current negotiations. But he added, "You will learn about it very soon."

Begin was much more effusive in talking about the upcoming intensified negotiations. He said: "We shall negotiate every day. Maybe, in those 40 days, as we hope, we may reach an agreement. If we do, we shall rejoice in it."

He stressed that no one can predict an agreement by May 26. But, noting that it took three months longer than originally planned to reach last year's Egyptian-Israeli peace treaty, Begin said, "Why be pessimistic in advance?" e

The sources said the new negotiating round will be led by the top negotiators of the three countries -- U.S. special ambassador Sol M. Linowitz, Egyptian Prime Minister Mustafa Khalil and Israeli Foreign Minister Yosef Burg -- and will begin during the week of April 27.

The tentative plan, the sources added, is for the talks to begin in the Tel Aviv suburb of Herzlya, continue there for 20 days and then, if necessary, move to the MENA House hotel outside of Cairo for another 20 days.

Left unclear was whether the new arrangements would provide sufficient flexibility to crack the deadlocks that have hampered the talks for 10 months. In addition to the functions of the self-governing authority, there are serious disputes over land and water usage, the size of the Israeli security force to remain in the area during the five-year period and Israel's right to continue establishing Jewish settlements in these territories.

At his press conference, Begin gave little sign that Israel is prepared to back away from its hard-line stands on the settlements or its determination to limit the powers of the self-governing authority in ways that would prevent the territories from evolving into an independant Palestinian state.

Israel's position, he said, was based on its vital security interests and its need to guard against terrorism from Palestinians bent on destroying the Jewish state. He said, "Hundreds of thousands of people would be killed if we are not responsible for security on the West Bank and Gaza."

However, U.S. sources said that, in private, Begin had shown unexpected willingness to explore all the disputed issues and seek to find ways of bridging the gap between the Israeli and Egyptian negotiating positions.

The resultant optimism expressed by these sources in private was hinted at publicly by Carter, who, while stressing that "we have a long way to go," added: "We are delighted at the progress that has been made."