Saudi Arabia has decided on an immediate oil price rise equaling windfall profits by international companies, and that is by no means the worst energy news from the Persian Gulf coinciding with the Iran crisis.

The still unspecified price rise is no surprise but had not been revealed to U.S. officials. Sheik Zaki Yamani, Saudi Arabia's petroleum minister, disclosed it to us in an interview at his spacious villa in Jeddah. Much more ominous are hints from Saudi officials that the United States cannot count indefinitely on present high Saudi oil production unless there is progress on the Palestinian question.

This is the prospect from America's best friend among big oil-producing Arab states, a nation that views with pride a special relationship with Washington. Elsewhere on the Persian Gulf, the certain prospect is higher prices and lower production in countries that now pump less oil for more money than the Saudis. Finally, Saudi experts bet privately that final resolution of the hostage crisis in Tehran will significantly reduce oil to the West.

Against this background, the imminent Saudi price increase is not significant economically but does move away from determination here to hold the price line. The reason given us by Yamani -- that the Saudis did not keep prices down just to increase the profits of the oil companies -- duplicated statements to Treasury Secretary G. William Miller on his recent visit here. Yamani says the oil companies can absorb the increase by reverting to previous profit levels, a claim the industry vigorously denies.

The question, then, is: how big a price increase? As we were ushered out of Yamani's study, three oil ministry officials entered to start calculating exactly how much of their price restraint has become profit for the companies -- and then increase prices that much. That's the man who says we must have this increase, said Yamani, pointing to one official. Not an increase, the aide protested. Only an adjustment.

There is no link of this adjustment to events in Tehran. Saudi officials are appalled by Ayatollah Khomeini and do not believe his demand to reduce oil production for the West (accompanied by personal denunciation of Sheik Yamani) will be heeded by other producing states. Even so, reduced production throughout the Gulf is regarded here as inevitable.

That will be dictated by technical reasons and market forces. Add to that what Saudi experts believe will be drastically reduced Iranian oil before the crisis is over. Believe me, one official told us, it won't affect just the Japanese or the Germans. You too will be hurt.

Accordingly, it is critical whether Saudi Arabia keeps pumping oil at its present high level of 9.5 million barrels a day. That rate is attacked here by conservatives, nationalistic students and prominent economists as contrary to Saudi interests. It is sustained by the regime both because of the special relationship with the United States and the realization that the kingdom's long-term prosperity depends on a healthy western economy.

It is here that the subtle connection between Israel and Saudi oil comes into play. The Saudis never have quite recovered from the shock of Camp David and feel that President Carter today has set aside the Palestinian question. They expect nothing to be done before the 1980 presidential election and are pessimistic about progress after that.

Official Saudi policy, as pronounced by Crown Prince Fahd, denies that oil production is affected by the Palestinian question. In private, the answer is shaded. We have been giving a quid without getting a quo, one cabinet member told us. There is a question of how long this can continue.

Moreover, the Saudis' apprehension over Washington's freeze of Iranian assets is deeper than they or U.S. officials publicly admit. Secretary Miller's promises during his visit that this could not happen to Saudi Arabia were not entirely reassuring. "Let's say that I am not relaxed," Yamani told us.

Lack of relaxation is explained by another Saudi official who compares present investment in the United States with putting savings in a bank that might well confiscate the account. One deputy cabinet minister believes fear here will become acute if Iranian assets remain frozen even after the hostages are released.

But the most disturbing change in the mutually dependent U.S.-Saudi relationship is the pervasive feeling by leaders here that Uncle Sam is on the run worldwide. That perception transcends even oil economics and is the subject of our next column from here.