The slow-moving shuttle negotiations on a Middle East peace settlement took a new turn yesterday when a confidential letter from Egyptian President Anwar Sadat was handed to Israeli Premier Menachem Begin.

U.S. special envoy Alfred Atherton handed the letter to Begin and reported briefly on his talks in Egypt Wednesday with Sadat and Foreign Minister Mohammed Ibrahim Kamel.

Neither Begin nor Atherton would tell reporters what the message was about. "But I will reply to it early next week and Mr. Atherton will be able to take my reply back to Egypt on Tuesday," Begin told reporters.

"You will understand," he said, "the contents of the message must be kept confidential. I'm sorry this will increase the curiosity of the press but I can't help it."

"Since the breakup of the foreign ministers' political committee in Jerusalem last January, Atherton has been moving between Cairo and Jerusalem trying to obtain agreement on a declaration of principles to govern Middle East peace negotiations.

He is to visit Amman today in an effort to discuss current peace moves with King Hussein.

The Jordanian government has repeatedly declared that it will not participate in the Egyptian-Israeli peace talks unless Israel commits itself at least to total withdrawal from occupied Arab territory and recognizes Palestinian rights to self-determination.

According to reports in Jerusalem and in Cairo the negotiations have run into persistent blocks on those two issues.