King Hussein of Jordan yesterday insisted that the Palestine Liberation Organization must be recognized as "the legitimate representative" of the Palestinian people in any expanded negotiations with Israel, dealing a new blow to hopes for reviving the Mideast peace process.

In a closed-circuit television address to the annual meeting here of the National Association of Arab Americans, Hussein reiterated that the PLO must have a major role in any joint Jordanian-Palestinian delegation that would negotiate with Israel on the status of the West Bank and Gaza Strip.

"It is the consensus of the Palestinians that the PLO is the legitimate representative in any negotiation determining their future," Hussein said in the live telecast from Amman. "We are their partners according to their choice. We will never take away their right to represent themselves."

Hussein's remarks were another indication that his Feb. 11 proposal for expanded peace talks, made jointly with PLO Chairman Yasser Arafat, is linked inextricably to conditions that neither Israel nor the United States is willing to meet.

In compliance with pledges to Israel, the United States has said it will not deal with the PLO until it recognizes Israel's right to exist.

Hussein also said that any new talks "should be conducted under international auspices . . . where every country with a legitimate interest in the region would be able to participate." That idea also is opposed strongly by the United States and Israel because it would permit the Soviet Union to use the peace process, from which it has been excluded for almost a decade, to increase its influence in the Middle East.

The Feb. 11 Hussein-Arafat accord initially raised cautious hopes here about the possibility of a Jordanian negotiating team that would include Palestinian spokesmen who were not members of the PLO. But when Assistant Secretary of State Richard W. Murphy visited the area to explore that possibility, it became apparent that the PLO was insisting on the right to name the Palestinian negotiators.

That was acknowledged by Secretary of State George P. Shultz, who told The Washington Post in an interview last week, "An effort was made, but it didn't quite come off."

Shultz insisted that the possibility of eventually getting a delegation acceptable to all sides is "still very much of a live question," but Hussein's remarks yesterday indicated that the Arabs are unwilling to show flexibility.

Hussein, backed by such other moderate Arab leaders as Egyptian President Hosni Mubarak, has been calling for the United States to pressure Israel into allowing the PLO into the process, either directly or through recognition of its right to choose the Palestinian negotiators.

The king said yesterday that he will continue to press that point when he meets with Shultz in Amman next Sunday. He also acknowledged that he plans to visit the United States later this month for his son's graduation from Brown University and expects at that time to talk with President Reagan.