Secretary of State George P. Shultz reacted cautiously yesterday to remarks by Palestine Liberation Organization Chairman Yasser Arafat that he is ready to accept a U.N. Security Council resolution recognizing Israel's right to exist in exchange for a U.S. endorsement of the right of the Palestinian people to self-determination.

"Probably the attitude of the Palestinians has been shifting some -- I hope so," Shultz said aboard his plane en route home from a meeting in Vienna with Soviet Foreign Minister Andrei Gromyko.

Arafat said in an interview Tuesday that he would accept Resolution 242 if the United States explicitly endorsed Palestinian "self-determination."

Asked about Arafat's comments, Shultz responded, "The word 'self-determination' has come, in the context of the Middle East, to be the equivalent of an independent Palestinian state," which the United States opposes. Therefore, he said, Arafat's statement contains "a terminal logical probem." But he added, "It's good to have people say the word 'Israel' and the word '242.' "

In Washington, State Department spokesman Edward Djerejian said, "It is U.S. policy that any agreement must address the legitimate rights of the Palestinian people. . . . On the crucial issue of governance, it is the firm view of the United States that the best chance for a durable, just and lasting peace is offered by self-government by the Palestinians of the West Bank and Gaza, in association with Jordan."