The prospect of a vast and untapped global supply of oil beyond the control of the existing energy cartel is ecasting a powerful lure in such staid instituitions as the World Bank, the United Nations and the U.S. Treasury Department.

This new hope centers on the oilproducing potential in the undrilled regions of Africa, Latin America and Asia.

Already the World Bank has embarked on a $3 billion funding program in these regions which its energy experts believe could raise world production by 6 million barrels a day, the equivalent of Iran's production before the coup.

All this would seem to fit the prescription written five years ago for the United States and other industrial nations when crude oil prices quadrupled against a background of shrinking reserves. What could better fit the bill than a new and globally diversified supply base for the would's crude oil consumers?

There are already strong stirrings of discord among big oil, the Carter administration and the World Bank over the exploration-financing program as well as the share of the international oil companies in tapping the new supply source.

In January the chairman of the world's largest oil company, Exxon's Clifton Garvin, privately called on Treasury Secretary W. Michael Blumenthal to urge that the bank's program for the non-OPEC countries be abandoned.

He told Blumenthal that such programs of exploration for oil and gas are "inherently risky" and "ill-suited to bank lending." Should the World Bank wish to go forward nonetheless, Garvin told the tresury secretary, it should insure that drilling opportunities were "first offered to industry on reasonable terms." Blumenthal serves as a U.S. director of the international lending organization.

World Bank and Carter administration officials were surprised at Garvin's plea.

Promise of new Third-World oil coming into world markets also means downward pressure on prices, and undercutting tth OPEC grip.

Blumenthal did not follow garvin's advice and the bank program, earlier endorsed by the Bonn Summit, was approved.

What was curious about Garvin's argument, however, is that two months later Exxon took a different tack. In an announcement that sent tremors through international oil circles, Exxon said it would no longer be selling crude oil to European and Japanese companies in the 1980s. Supplies then would be too tight, Exxon said.

This episode illustrates vividly the most compelling energy question facing the nation: can we avert a world oil shortage by developing oil resources outside of OPEC? And, if possible, will it be with or without the major oil companies?

The outlines of an answer are entwined in the explanations of why Exxon would be discouraging future oil production, while at the same time planning future cutoffs in its oil sales-paths that appear contradictory.

William Slick, an Exxon vice president, explains: "We're not against oil development...we're against loaning money through the World Bank to national companies that complete against our private companies."

A sterner assessment of Exxon's motives is offered in a February Congressional Budget Office report: "Guaranteed loans from the World Bank and other sources can only damage further the competitive position of the international oil companies," the CBO said.

Does this mean that the world must forgo added oil production unless the major oil companies do it? Blumenthal answered no.

Still other questions remain, however.Do companies like Exxon and the other majors have a continual incentive to seek new oil production? On this point, the CBO study, "A strategy for Oil Proliferation: Expediting Petroleum Exploration and Production in Non-OPEC Developing Countries," suggest that the answer may also be no.

The CBO says there are two reasons why "the companies might deliberately ignore prospects," for oil production in developing countries. "By restraining supplies prices are kept high" and "the companies see their futures as marketers for OPEC and do not want to jeopardize their status by negotiations with potential competitors."

CBO's suggestion is reinforced by a disclosure Exxon made at a Senate Foreign Relations subcommittee hearing several years ago. Asked by Sen. Charles H. Percy (R.-i11.) why Exxon did not develop what company geologists suspected could be 10 billion barrels of oil reserves in Oman, Exxon executive Howard Page said, "I might put some money in it if I was sure we weren't going to get some oil, but not if we were going to get oil because we are liable to lose the Aramco concession."

Aramco, the Arabian American Oil Co., is made up of Exxon, Mobil, Standard Oil of California and Texaco, and produces most of Saudi Arabia's oil. Page, in other words, said Exxon did not want to increase oil production if it jeopardized relations with the Saudis, or forced a reduction in Saudi oil production.

There are occasions then-if the CBO is right-when the major oil companies could act, either consciously or inadvertently, as obstacles to increasing oil production and finding new oil supplies.

If the suggestions posed by CBO and the incident cited by Page are correct, oil companies are not likely to develop new supplies that would threaten their market shares or profit margins.

Setting aside the issue of the companies' role, the great challenge confronting the world, if Energy Secretary James R. Schlessinger Jr's warnings of a 1980s oil squeeze are correct, is how to increase non-OPEC oil production.

Garvin's letter added still another argument why the United States should oppose the bank program. "Industry activity in these [non-OPEC] countries has been extensive," Garvin wrote.

World Bank officials and the U.S. Geological Survey's Bernardo Grossling dispute this, contending that that Third World countries today are still largely unexplored frontiers with enormous prospects for new oil and natural gas discoveries.

Among their arguments:

There are better prospects for major oil discoveries in the non-OPEC developing countries than in the United States and other industrial states, according to the World Bank. Grossling says that over the last three decades, the oil discovered per well drilled in the United States averaged 15,20 and 30 barrels per foot drilled.

In Western Europe, including the North Sea, it has been 100 to 200 barrels. And in Africa, it has been a staggering 500 to 1,000 barrels found for every foot of exploratory drilling. The United States, on the other hand, with 6 percent of the prospective drilling area, has been the center of two-thirds of the world's oil drilling.

As for the rest of the world?There are twice as many oil wells in Kansas as in all of Latin America, and three times as many wells in Arkansas as in all of Africa.

Despite the 5-fold increase in world oil prices since 1973, trends for seismic work and exploratory drilling heve remained nearly level or have declined. From 1973 to 1976, exploratory drilling in non-OPEC Latin America dropped from 9.1 wells per 100 square miles to 8.5.

During the same years in non-OPEC Africa, the drilling rates remained at 2.8 wells per 100 square miles of prospective areas.

"The bulk of the drilling has been done mostly in the United States, followed by Canada and Mexico, since the embargo," Grossling says, adding that "The OPEC countries' [drilling activities] are also way down."

Grossling concludes that the drop in exploratory work "has nothing to do with geology."

Still other reasons are offered why major oil companies have not explored as widely in the non-OPEC nations.

William Lane, head of DOE's office of Competition, says "There has been a significant market failure, the laissez faire system the companies operated under has broken down." New mechanisms and new assurances are needed, Lane says, for moving private investment into oil exploration where it is needed overseas.

Lane's view is shared in part by Lehman Bros.' Martin Roberts, who talks about the "great structural changes" in world oil markets over the last 25 years. Roberts points out that today more than 60 national oil companies control about 80 percent of the world's oil reserves, versus 20 percent two decades ago.

The rise of OPEC's power and economic nationalism are other factors. Even then, major oil companies are also exposed to unexpected risks abroad. One major, for example, recently found oil in the Cameroons, only to learn afterwards that the Yaunde government changed the terms of their original agreement once they knew oil was found.

Efrian Friedman , head of the World Bank energy program, said in a recent interview, "Our diagnosis that there was a problem with exploration has been correct." To turn that around, the Chilean seientist says, "The main thrust of our program has been to facilitate the access of the oil industry to the developing world."

This means not only insuring that the host countries have equitable agreements with the oil companies, but also identifying energy projects the bank can provide seed money for.

Loans have been made to India, Thailand and Pakistan, and nearly 15 other countries have expressed interest in projects ranging from oil exploration to production.

Equally important, the bank has taken on the role of "honest broker" in negotiations between Gulf Oil and Pakistan, a deal concluded satisfactory to both parties, and has been approached to help in other negotiations.

Knowledgeable sources also say that since the bank program was approved a number of companies have asked the bank to help gain access to countries that have resisted negotiating with majors.

"The thinking in the industry is changing very fast," Friedman says.

How fast that thinking changes likely will determine the outcome of the world energy production over the next years. CAPTION: Picture, Symbolic of the prospects for oil production beyond the Organization of Petroleum Exporting Countries is this tanker being loaded at Coatzacoalcos, Mexico.