Egyptian President Anwar Sadat provided details yesterday of his plan for rapproachement between Israel and the Palestinians, and made clear that he is undeterred by the Reagan administration's cool reaction in two days of official talks.

At a press conference at Blair House , Sadat also hinted that he expects a delay until year's end in new momentum toward Middle East peace, including progress in the Egyptian-Israeli talks on Palestinian autonomy.

"I never anticipated there would be a prompt answer" by President Reagan to his new proposals on the peace process, said Sadat, who described the U.S. president as "amiable," "sincere," "conscious" and a man who deals with the "broad lines" of polic without immersion in detail.

Ccording to Egyptian sources, Reagan said very little in response to Sadat's proposal for U.S. contacts with the Palestine Liberation Organization. These sources said it was Secretary of State Alexander M. Haig Jr. who reiterated in detail to Sadat the six-year-old commitment to Israel not to recognize or negotiate with the P.L.O. In a press conference Thursday, Haig attributed the remarks to Reagan.

Haig, not taking Reagan's comments as a definitive rejection, said yesterday the U.S. president needs "ample time to study" his suggestions and to consult other Middle East leaders, including Israel Prime Minister Menachem Begin, King Hussein of Jordon and Crown Prince Fahd of Saudi Arabia, who are expected here in September, November and December, respectively.

Asked about the resumption of the stalled Egyptian-Israeli talks on Palestinian autonomy, Sadat said that after Reagan's meetings with these other leaders it will be time to give new momentum to the peace process, initially through discussions at the ministerial level. A possible American-Egyptian-Israeli summit meeting, he added, "must be preceded by intensive efforts."

In the 45-minute discussion with reporters on his last full day in Washington, Sadat made clearer than ever that his essential aim has been to place the Palestinian problem on the agenda of the Reagan administration, which has shown signs of seeking to ignore it. Through a combination of fortunate timing and charisma, Sadat appears to have made substantial strides toward his goal.

In his remarks yesterday, as in his private talks with Reagan last Wednesday and Thursday, Sadat argued that the recent cease-fire in Lebanon involving Israel and the PLO was "a very important and significant turning point" that provides the basis for a drive toward a settlement of the Palestinian problem.

Specifically, Sadat has said that U.S. contacts with the PLO would encourage moderation in the Palestinian leadership and thus build on the cease-fire toward "the next step" in the Sadat scenario, "the mutual and simultaneous recognition" by the Israelis and the Palestinians.

Despite Sadat's use here last week of the Lebanese cease-fire as his rationale for new steps, his proposal for Israeli-Palestinian mutual recognition goes back to the third week of January. The plan was previously offered by Sadat, without much notice here, in a Feb. 10 address to the European Community initiative launched in 1980 a "turning point" that invited further steps to bring a rapproachment between Israel and the Palestinians.

The Egyptian leader is also reported to have discussed his plan with Begin in their meeting June 4 and to have received the expected negative reaction. According to informed sources, Sadat also sent word of his idea to PLO leader Yasser Arafat and other senior Palestinians through emissaries prior to the sudden upsurge of fighting in Lebanon last month and the cease-fire.

Sadat said yesterday that his idea of "mutual and simultaneous recognition" does not necessarily encompass formal Israeli recognition of the PLO as an organization, which is anathema in nearly all public opinion in the Jewish state.

"Israel is to recognize the fact that the Palestinian question is not as humanitarian question as stated in [United Nationa] Resolution 242 [but] it is a political question with all dimensions and that the Palestinians deserve a homeland. The Palestinian said must recognize Israel within its borders and live and coexist with it," Sadat explained at the press conference.

In a prepared address late yesterday at Georgetown University, where he received an honorary degree, Sadat followed through on the theme: "We are asking all nationa of the world to talk to the Palestinian people and their representatives, endorsing every cease-fire and encouraging a more stable Middle East, telling both the Palestinian people and the Israeli that they should sit together and talk together to settle their problems without shooting out their grievances."

Sadat, who discussed his ideas with British leaders in London en route to Washington last week, is expected to take them to Begin in more definite terms in an Alexandria, Egypt, meeting in the next few weeks. Later Sadat is expected to discuss them with West German, Austrian and French leaders.

The policies of Begin's newly formed government, including its recent reassertion of the Israeli territorial claim to the occupied West Bank and Gaza, could create new obstacles "for sure," Sadat told reporters yesterday.

At the same time, the Egyptian leader has consistently expressed confidence in the ultimate success of the peace process. "Patience and perserverance" are essential elements in resolving the seemingly endless dispute between Israel and the Arabs, Sadat told a news conference late Thursday.

Sadat's new plans for politic al change involving the Palestinians are not as dramatic or as visual as his startling opening to Israel, symbolized by his journey to Jerusalem in 1977. But like the earlier turn, Sadat's new ideas could change the situation in the Middle East in basic fashion, if they are accepted. In this efforts, he is using both the public relations flair and the persistence he employed earlier.