Vice President Bush and Saudi King Fahd agreed today on the need to reestablish stability in the chaotic oil market but failed to agree on a desirable price for a barrel of oil or on any common measures the two governments might take to stop plunging oil prices.

Following a 2 1/2-hour meeting between the two leaders at the king's palace here, a senior administration official said the two had held a general exchange of views on oil and other regional issues during which the vice president explained the administration's concern that falling oil prices had become a threat to U.S. national interests.

Bush made it clear that Saudi interests and U.S. interests are "not identical" on oil prices, the official said, adding that the talks were "open" and that positions were "frankly put."

Earlier, Bush, indicating that "the free fall" of oil prices had become the focus of his talks here, reiterated his view that the plunging prices pose a threat to U.S. national security as well as "a problem" worldwide.

He also indicated that President Reagan shared his sentiments, saying, "I feel it, and I know the president of the United States feels it."

Seeking to clarify his controversial comments in Washington last Tuesday, the vice president told a group of American businessmen in the Saudi capital of Riyadh this morning that he had not come to the kingdom on "a price-fixing mission" or with "a simple and easy answer" to how oil producers should seek to stabilize the market.

"But I hope when I leave this part of the world I will have a clear idea of how the countries involved -- and one major one is Saudi Arabia -- how they feel there can be some stability to a market that certainly can't be very happy to them," he said. While declaring that low energy prices are desirable, he said, "there is some point at which the national security interest of the United States" requires "a strong, viable domestic industry."

Bush's private meeting with the Saudi monarch came after a formal dinner with the king and marked a schedule change from a planned Monday working session.

At a three-hour private dinner last night at the U.S. Embassy in Riyadh, the vice president discussed the oil situation in great detail with Saudi Petroleum Minister Ahmed Zaki Yamani and other Saudi government ministers.

Bush's press secretary, Marlin Fitzwater, said that "much of the focus of discussion related to oil prices and production" and that the two sides had "shared their views about the recent decline of oil prices."

While Bush made no specific request of the Saudis, Fitzwater said, the vice president expressed both his desire to see market forces work and the administration's concern "to ensure a strong domestic oil industry as part of fundamental U.S. national security interests."

During the session with the American businessmen in Riyadh this morning, Bush also disclosed that King Hussein had been so upset with congressional rejection in late January of the administration's proposed $1.9 billion arms sales to Jordan that he "kind of broke off discussions" with the United States.

So angry had the king been with Washington following that rejection, that at one point recently he refused to receive Assistant Secretary of State Richard Murphy.

Admitting the administration had broken its promise to sell arms to Hussein but blaming it on Congress, Bush said, "He has a heightened sense of frustration with us about this kind of thing."

But, he added, "the door is wide open" to the Jordanian king, whom he described as "a courageous figure."

Bush said that the administration planned to "do everything possible" to assure the passage in Congress of its request for $354 million in arms sales to Saudi Arabia, which pro-Israel congressmen are seeking to block.

"It is in my view essential to our own selfish national interest that this arms sale go through," he said.

The main announced objective of Bush's trip to Saudi Arabia and three Persian Gulf states is to reaffirm the U.S. commitment to their security at a time of renewed escalation in the Iran-Iraq war.

The Saudi security concern was underlined today by reports that a 17,000-ton Saudi tanker had been badly damaged by what was believed to be an Iranian air strike as it was sailing off the coast of Qatar.

Bush said in a short speech to the American businessmen that the United States took the security of the Arab gulf states "very seriously" and that it remained "fundamentally, irrevocably" committed to the free flow of oil through the gulf.