Israeli Defense Minister Ariel Sharon said yesterday that his army's victory in Lebanon opened the way to a new era of "peaceful coexistence" with Palestinians on the West Bank and in the Gaza Strip, but two Palestinian leaders in those areas declared his view to be "an illusion."

The exchange came in an unusual display of intercontinental electronic wizardry that enabled American television viewers of the Sunday network panel shows to see and hear -- all within 90 minutes -- a succession of major actors in the next stage of Middle East diplomacy.

Sharon appeared twice, on "Face the Nation" (CBS, WDVM) and "This Week with David Brinkley" (ABC, WJLA). King Hussein of Jordan also appeared on the Brinkley program, via satellite from Amman. "Meet the Press" (NBC, WRC) sent moderator Bill Monroe to Israel to interview Bethlehem Mayor Elias Freij and former Gaza mayor Rashad Shawa, who had been denied permission by Israeli authorities to travel to the United States to present their views on last week's program.

Sharon, who was in the final hours of a visit to Washington, said the "terrorism" of the Palestine Liberation Organization has been "the main obstacle to future peace and peaceful coexistence with the Palestinian Arabs." Referring to his meetings last week with representatives of Israeli-backed "village leagues" on the West Bank, Sharon suggested that the way is now open for a political settlement there with moderate Palestinians.

Freij and Shawa, two widely accepted leaders in the West Bank and Gaza territories that have been occupied by Israel since the 1967 war, were quick to challenge Sharon's view of the future.

The people whom Sharon met on the West Bank, said Freij, the elected mayor in Bethlehem, are "nobody." At another point he said, "The Israelis have created these creatures the village leagues . They are protecting them, just as symbols. These collaborators will simply sign a blank check for Israel."

In recent days, Sharon has hinted that Israel, invoking its own interpretation of the Camp David accords, may forge an agreement with village leagues in the West Bank and Gaza even if the four-year-old autonomy talks involving Egypt and the United States remain deadlocked.

Freij charged that any agreement reached in this fashion would be "a dictation" by Israel.

Shawa, who was the appointed mayor of Gaza until his ouster by Israel a month ago, conceded that "for the time being" the Jewish state has the physical power to impose its will on the West Bank and Gaza.

But he said Palestinians will never accept this and will continue to seek self-determination and a Palestinian homeland there.

Both Freij and Shawa expressed support for the PLO, saying it is the accepted representative of the Palestinian people. The Bethlehem mayor said the PLO should now concentrate in a political area, especially on "a Palestinian political initiative."

As part of the discussion of next steps, Sharon and other Israeli officials have recently called Jordan "a Palestinian state," indicating there is no need for another Palestinian entity in the West Bank-Gaza.

As he did in a meeting with Secretary of State George P. Shultz Friday, Sharon repeated that Israel will never accept a "second Palestinian state" in the area.

Israeli radio reported yesterday that U.S. officials suggested to Sharon during his talks in Washingtion that there should be a demilitarized Palestinian state in the West Bank and Gaza.

The report quotes Prime Minister Menachem Begin as saying that "any attempt to alter the Camp David agreements by introducing the idea of self-determination would lead to the collapse of the agreements," and also quotes an unnamed minister as suggesting that such a move would result in annexation of the territories.

Hussein, rejecting Sharon's statements, said that Jordan has given a temporary home to Palestinians "awaiting the resolution of their problem on their legitimate soil."

The Jordanian monarch added that the central and unresolved issue is that of "legitimate Palestinian Arab rights on Palestinian soil under occupation by Israel in the West Bank, Arab Jerusalem and Gaza."

Hussein expressed hope for a political dialogue on the Palestinian problem in the wake of the Beirut battles.

If there is no success along these lines in the near future, he said, the result could be "disaster that will overtake all of us in the entire area and maybe the world."

Sharon, who joined the Brinkley program immediately after the interview with Hussein, lamented that "being neighbors, being so close, we have to talk through the television."

On other points, Sharon also said:

* The PLO is planning to leave behind "2,000 to 3,000 terrorists" in Beirut to prepare a nucleus for continuing military actions. He did not suggest that Israel will resume operations because of this and said, "We have finished our task" in Beirut.

* Israel "will stay in Lebanon as long as Syrians will stay there." He expressed hope this Israeli presence will be "kind of a pressure" on Syrians to leave and displayed no enthusiasm for new Israeli-Syrian battles.

* He believes Lebanon will sign a peace treaty with Israel after the installation in office of Christian militia leader Bashir Gemayel, who was elected Lebanese president last week.