Israel's Cabinet named Foreign Minister Moshe Dayan and Defense Minister Ezer Weizman yesterday to head the Israeli delegation to peace talks in Washington on Thursday.

Dayan is already in New York for a speech at the U.N. General Assembly today and Weizman is to leave Israel this morning.

Prime Minister Menachem Begin, who has been resting at home since the parliament approved the Camp David peace plan, did not attend yesterday's Cabinet session. Aides said Begin is not ill but "fatigued" from the recent summit meeting and its aftermath.

The Cabinet, by restricting the delegation to only two ministers, put an end to several days of inter-party manuvering, during which each of the factions in the coalition government sought to be represented in the peace talks with Egypt.

Left out, for the time being at least, were Deputy Prime Minister Yigael Yadin, of the Democratic Movement party, and Interior Minister Yosef Burg, head of the National Religious Party.

Yadin had said over the weekend that only "functional" delegate should attend the summit followup, and that those most directly involved are Dayan and Weizman. A team of lawyers and special aides will accompany the two.

The Cabinet did authorize the ministerial defense committee to represent Israel in Washington if needed in the later stages of the talks.