A menacing stalemate is in effect in a critical chess game between the United States and Saudi Arabia over future oil supplies.

American political and business officials here are warning that unless the situation is resolved, the United States, Western Europe and Japan face the prospect of catastrophic price increases and oil shortages in the years immediately ahead.

One forecast, attributed to Saudi Petroleum Minister Zaki Yamani, is that a worldwide production shortage could drive up the price of oil to a minimum of $30 a barrel as early as 1980. The present price is about $13 a barrel and even at that level the U.S. bill for oil imports has reached $45 billion annually.

Another forecast, orginating with the U.S. government , is that by 1985 world demand will exceed the world supply by roughly 8 million barrels a day unless the Saudis approximately double their present level of production.

That is the present focus of an intensive U.S. diplomatic effort to persuade Saudi Arabia to increase its oil output from 8.5 million barrels daily this year to more than 16 million barrels daily by 1985. This would involve capital expenditures of at least $8 billion by the Saudis and a construction program that must begin soon.

The Saudi government so far has not agreed to any increase in production and, in fact, argues that its own interests would be better served with a production level of no more than 5 million barrels a day. That much oil, they maintain, provides them all the money they need. The also maintain - and the Americans agree - that their oil is far more precious in the ground, where its value will appreciate enormously, than on the world market at $13 a barrel.

Differences of opinion exist in the United States over the possibility of oil shortages. There has been a wave of speculation in oil industry circles that the current world oil glut will continue in the 1980s, fending off suggestions of a severe shortage.

Central Intelligence Agency projections of a world oil shortage, which are tied in part to predictions that the Soviet Union will become a significant oil importer in the mid-1980s, have been discredited in private by Energy Secretary James Schlesinger.

There is universal agreement here that the real sticking point is not money but the Arab-Israeli conflict. "If the United States will get from Israel a Palestinian homeland," said an official at the highest level, "you can get all the oil you want. If you don't get a settlement, I don't know what will happen."

There is a widespread belief in this country that the United States has the power to exert effective pressure on Israel to withdraw from Arab territories it has occupied since 1967. That pressure, it is said, could take the form of sharply reduced financial and military assistance to Israel. It could also involve massive military assistance to Egypt.

The failure of the Carter administration to exert or threaten to exert these pressures has produced a sense of impatience among the Saudis and an unwillingness to make any commitments on future oil supplies.

They have given no ultimatum to the United States, according to U.S. sources, and they have not made production increases a quid pro quo for a Middle East settlement. There is an unspoken understanding, however, that this is the key issue.

One of the big frustrations of Americans here, and some Saudis, too, is their belief that the United States is living in a fool's paradise as far as energy is concerned. No U.S. energy conservation program has been adopted U.S. oil consumption rises each year and the country is now dependent on imports for nearly half of its supplies - about 7 million barrels a day. Within seven years, the U.S. import need is projected at 12 million barrels a day. That extra 5 million barrels, it is argued here, can only come from the Saudis. No other country can take up the slack.

The Saudis have a vested interest in that argument. It is the big card they have to play in nudging the United States toward their position on the Israeli-Palestinian question.

But it is an argument that American diplomats here have bought and are pressing hard on the White House and the State Department.