President Carter, in an unusually warm and explicit statement, yesterday began his peace-seeking talks with Israeli Prime Minister Yitzhak Rabin by endorsing Israel's demand for "defensible borders."

Israeli officials were openly elated at Carter's unexpected repetition of a phrase that has long been used by Israel in arguing against returning all of the Arab territory that it captured in the 1967 war. "I was pleased to hear it," said Rabin later.

The White House declared later that Carter's extemporaneous remark on the White House lawn did not represent a change in the U.S. position on the territorial aspects of a Middle East peace settlement.

Carter spoke of defensible borders for Israel severl times during his presidential campaign, stating on some occasions that he would support Israeli refusal to relinquish control of the Golan Heights, which was captured from Syria, or control of the Christian and Jewish holy places in old Jerusalem, which were taken from Jordan. However, this was the first time that Carter spoke publicly of Israel's need for "defensible borders" since becoming President.

Carter's view during the campaign was that the first step toward an ultimate Middle East peace should be such an absolute U.S. assurance of Israel's security that all Middle Eastern parties would take this as a starting point. His strong endorsement of Israel and its leadership yesterday appeared to be in keeping with this idea.

With Rabin by his side, Carter spoke of "the close historic ties" between the two countries and "our commitment to Israel, our long-standing friendship, our sharing of democratic principles and human liberty, and our constant search for peace."

He also spoke of "our complete commitment to an even greater interrelationship on a common basis with the courageous citizens whom you [Rabin] represent in the great nation of Israel."

Carter went on to say that "1977 is a year that might very well bring a major step forward toward ultimate and permanent peace." He declared that Secretary of State Cyrus R. Vance had recently begun the U.S. exploration of a future permanent Middle East peace "so that Israel might have defensible borders so that the peace commitments would never be violated, and that (there) could be a sense of security about this young country in the future."

The Israeli leader responded by declaring that "peace is our highest aspiration" and by quoting words of Solomon in the Book of Proverbs, that "Righteousness exalts a nation." This drew a slight smile from Carter, who has spoken of the biblical link to the Holy Land and who keeps a Bible on his desk in the Oval Office.

After 92 minutes of discussions with Carter, Vance and the other high officials in the Oval Office and "a working luncheon" and a business meeting with Vance at the State Department, Rabin told reporters that "I am sure that we will see a period of closer cooperation between our two countries."

He declined to make substantive comments about the discussions because they were to continue at a "working dinner" at the White House last night and another session with Carter in the Oval Office today.

A White House statement said Carter and Rabin agreed that the U.S.-Israeli relationship "forms a natural basis for exploring how best to move the peace process forward." The statement said the two leaders agreed that "it is important to make progress in 1977" toward a settlement of the Arab-Israeli conflict and that they agreed to work toward reconvening a Geneva peace conference in the second half of this year.

Both sides said no bilateral issues - such as economic aid and Israel's request for additional weapons - had been discussed a the White House yesterday. But such topics were discussed by Rabin in his separate meetings with Vance and Defense Secretary Harold Brown, and might well come up at the White House meetings today, sources said.

Arab leaders of Egypt, Saudi Arabia and Jordan are expected to visit Washington for Middle East peace discussions with Carter, and Syrian President Hafez Assad is expected to meet Carter for similar discussions in Europe in May. Officials said the other visits, like Rabin's, would be "working trips" with a minimum of protocol.

Carter called yesterday's stripped-down official welcome, with no honor guard of troops, no flag-waving government workers on the White House lawn and no waving by the leaders from the South Portico, part of "a different kind of visit" which emphasizes work rather than ceremony. For this reason last night's White House meal was listed as "a working banquet" rather than a formal state dinner with entertainment and high fashion.

Carter's reference to "defensible borders" for Israel was not the first time that phrase has been used by a U.S. chief executive. In July, 1970, then President Nixon, for example, used it in a television interview.

In the recent past, however, U.S. officials have usually spoken of Israel's need for "secure and recognized boundaries," which is the language United Nations Resolution 242 applied in 1967 to the territorial needs of all Middle Eastern states. A White House official conceded last night that "defensible borders" has come to be a code word of a special meaning in the Middle East confrontation.