The Reagan administration, faced with the Israeli cabinet's rejection of President Reagan's Middle East peace plan, nevertheless continued to express confidence yesterday that his proposals will become the basis for serious negotiations on resolving the Arab-Israeli conflict.

"It's hard for me to believe that Israel would reject the idea of peace," Secretary of State George P. Shultz said in reference to the plan outlined by Reagan Wednesday night. "It's hard for me to believe that they would reject the pledges of support for their security that the president gave. There are lots of things in that speech that are extremely important. And so total rejection is a word that I don't think is appropriate."

In Santa Barbara, White House spokesman Larry Speakes said, "We were aware that neither Israel nor the Arab states would find all parts totally acceptable. But the president has put forward the essential elements for progress toward a comprehensive peace."

The major elements of the plan outlined by Reagan in a nationally televised speech call for a freeze of Israeli settlements on the West Bank of the Jordan River, the eventual withdrawal of Israel from most parts of the West Bank and Gaza Strip and the granting of self-rule to the Palestinian inhabitants of these territories "in association with Jordan."

The initial reactions yesterday showed a mixed pattern, ranging from Israel's curt rejection to caution in the Arab world. In the United States, representatives of both Jewish American and Arab American communities were quick to express major reservations and concerns about the Reagan initiative.

Nevertheless, administration officials clearly were pleased by what they say they believe to be the long-term impact of his speech. They say the president has seized the initiative in the Middle East at a time when a unique opportunity for negotiation has been presented by the forced withdrawal of Palestine Liberation Organization forces from Beirut.

Domestically, some of Reagan's advisers said they believe the speech will reinforce his image as a forceful leader pursuing peace on the world scene.

The next step, administration officials said, is to move the parties involved to a dialogue and eventual new negotiations on the Palestinian question. Although the officials remained vague about how that will be done, they said they are convinced that Israeli Prime Minister Menachem Begin's government, despite its hostility, will take the proposal seriously as a basis for discussion.

"We know there will be discussion. We know there will be disagreement. But we know that we have advanced a proposal that can form the basis for movement," Speakes said.

Shultz, who made his comments during an interview on the ABC television program "Good Morning, America," underscored the administration's hopes that Jordan's King Hussein can be coaxed into the peace process from which he so far has stood aloof. While acknowledging that "we have no specific indication" about what Hussein will do, Shultz stressed, "He is studying it seriously."

Shultz, who appears to be emerging as the administration's point man in advancing the proposal, also held separate meetings at the State Department yesterday with the leaders of organizations from the Jewish and Arab communities in this country. In both cases he met with a generally negative response, which underscored how much work must be done if the administration is to overcome the animosities surrounding the Arab-Israeli conflict.

The National Association of Arab Americans welcomed those elements of the plan that would lessen Israel's grip on the occupied territories, but it added, in a statement, that it objects to Reagan's ruling out an independent Palestinian state and his refusal to recognize the PLO as "the legitimate representative of the Palestinian people."

Robert Joseph, the association president, said Reagan "has to go a step further" and begin a dialogue with the PLO.

Representatives of the larger and politically more potent American Jewish community took a different tack in their meeting with Shultz. Julius Berman, president of an umbrella organization that includes the chairmen of the major Jewish organizations in this country, said that, while Reagan's plan contained "a lot of solid points," his group had told Shultz that they found it "on balance, in terms of moving forward, not constructive."

Berman said that the Jewish leaders had emphasized their concern that the administration is making a mistake by taking positions that might prevent it from acting as mediator or honest broker in future Arab-Israeli negotiations.

"It is critical to that role that the United States not pre-ordain the ultimate results," Berman said. "It must retain the confidence of all the parties. It must maintain its independence. It must make recommendations not in advance, not in public and not in the glare of TV lights, where there is a danger of being frozen into positions that cannot be changed."

Reagan's plan got strong backing from former president Carter, who launched the Mideast peace effort at the Camp David summit four years ago. But Carter, who also was interviewed on "Good Morning, America," warned that top Reagan administration officials must play a strong role in advancing the plan.

"If they don't, it will go back even worse than before," Carter said. "If they'll stick to their guns, the answer is yes, there will be negotiations."

In a related Mideast matter, Sen. Mark O. Hatfield (R-Ore.), chairman of the Senate Appropriations Committee, charged that the administration illegally channeled $4.5 million earmarked for humanitarian assistance in Lebanon into helping to evacuate the more than 8,000 PLO fighters who left Beirut.

At a briefing on aid to Lebanon, Peter McPherson, administrator of the Agency for International Development, replied that the money was used as "bridge financing" to assist the International Red Cross. He added that the government expects the money to be repaid by Saudi Arabia, a supporter of the PLO, so that it then can be spent, as intended, on relief efforts in Lebanon.

McPherson also said the United States is increasing to $95 million its aid to help Lebanon recover from the war.