In its waning days, the Carter administration is trying to settle a controversial dispute with Algeria that has threatened the future of a multibillion-dollar U.S. investment in liquefied natural gas.

Five times this year, negotiators for the two countries have met and failed to agree on an acceptable price for the Algerian LNG, but U.S. hopes for a compromise have been lifted somewhat by Algeria's willingness to help resolve the U.S. - Iranian confrontation over the American hostages.

As of this week, there still was no agreement, however. And that is just fine for some administration critics like Sen. Howard M. Metzenbaum (D-Ohio), who argue that the Algerian LNG isn't worth the price the Carter administration is likely to pay. An LNG agreement would be a government bailout for the shipping and pipeline companies involved in the venture, they say.

In April, Algeria halted shipments of LNG to the United States after the Carter administration refused to accept Algeria's demands for a tripling of its LNG prices. The gas shipments had been arriving at terminals at Cove Point, Md., and Elba Island, Ga., since 1978.

Because of the stalemate, six huge tankers -- specially built at an average cost of $100 million apiece to carry supercooled LNG -- are tied up empty at ports in France and Greece. They represent an investment of more than $700 million by the U.S. Maritime Administration, which paid part of the construction costs and has guaranteed the ship construction loans.

The flow of regassified LNG from the two plants to consumers in Maryland and a dozen other states has been slowed to a trickle since April (the pipeline companies that operate the terminals can continue to charge their customers for the project's costs if it is still operating, even at a very reduced capacity). But the plant and its twin in Georgia appear to have no future unless the LNG shipments from Algeria resume. If so, the brunt of the losses would fall on the stockholders of the pipeline companies that operate the plants.

Finally, there are the vast facilities in Algeria that turn gas into a concentrated liquid by chilling it to minus 259 degrees Fahrenheit, reducing it to one-600th of its original volume for economic shipment by sea. The U.S. Export-Import Bank financed construction of the Algerian LNG facilities with direct payments of $1.6 billion to U.S. manufacturers that count as loans to Algeria at reduced interest. "They are a very good customer," said an Ex-Im Bank spokesman.

Although the spokesman said repayment of the Ex-Im Bank loans is guaranteed by Algeria's central bank, fully protecting U.S. taxpayers, failure of the LNG deal would nullify one of the Ex-Im Bank's major projects.

U.S. and Algerian representatives have not found an acceptable compromise between the $6 per thousand cubic feet that Algeria wants and a price the Carter administration will approve.

Energy Department officials will not disclose their top offer, but Metzenbaum says he believes it is $3.40 per thousand cubic feet in Algeria or $4.47 once the LNG has been regassified at the Eastern Seaboard plants.

That figure is three times the average price for domestic natural gas, Metzenbaum protests.

Metzenbaum, whose state stands to receive the largest share of LNG from Cove Point, has protested that Ohio consumers should not be forced to burn expensive LNG when there is plenty of cheaper domestic gas available. The difference between the $4.47 and average domestic natural gas prices amounts to an annual "overcharge" of $320 million in Ohio and $1 billion in all of the eastern states served by Cove Point, Metzenbaum contends.

To Metzenbaum, it is preposterous for the United States to remain dependent upon Algeria for a major source of its energy. Prior to the cutoff, Algeria was supplying about 1.5 percent of the U.S. natural gas demand, and gas industry officials had hoped that LNG deliveries would escalate by 400 percent by the year 2000. Those goals are seriously in doubt now.

The LNG project was conceived more than a decade ago, when the United States seemed to be rapidly running out of domestic natrual gas and when energy supplies in overseas Arab nations still seemed like promising substitutes. Now, higher domestic gas prices have caused a boom in drilling and a more optimistic outlook for future domestic gas production. The Energy Department and many members of Congress now favor greater reliance on gas shipments from Canada and Mexico rather than Algerian LNG.

Algeria's recent statements have added to that mood. One important Algerian official has said his country plans further price increases for LNG, bringing it in line with foreign crude oil prices, and ultimately, the price of electricity -- currently five times the price of domestic natural gas.

Metzenbaum contends that in trying to salvage the Algerian LNG agreement, the Carter administration really is bailing out the El Paso Co., the energy conglomerate that owns six operable LNG tankers.

According to a Carter administrtion source, the collapse of the LNG operation would not bankrupt El Paso. But the company is clearly suffering because of the termination of LNG deliveries. In July, it announced an 85 percent drop in earnings for the second quarter of 1980, from $40.7 million in the second quarter of 1979 to $6.1 million. It blamed the drop on the LNG cutoff.

El Paso says it remains optimistic that the price impasse will soon be resolved. If not, and the LNG project is discontinued, El Paso says it will face a loss of $375 million, most of that on its LNG tankers, a spokesman said.

And so the factors mount up, some favoring settlement, some arguing against one. "It's not a deal at any price," says an administration official, "because at some price, it's just not worth it."

In its public statements, Algeria remains one of the "price hawks" of the Organization of Petroleum Exporting Countries. Gas is a premium fuel -- one of the few ready substitutes for crude oil to which the industrialized nations can easily turn -- and its price must keep in step with crude oil, says Mourad Belgudj, Algeria's director of gas exports. If the United States doesn't like the price, no doubt Japan and European countries will be interested, Algeria says.

Privately, Algeria sounds somewhat less hardnosed, U.S. officials say. No longer a militant spokesman for the Third World, Algeria is exploring a more moderate middle ground in foreign policy, officials say, as evidence by its role as go-between in the hostage negotiations.

"Given their general principles [on pricing natural gas], they are trying in a good-faith manner to work something out. They want to get rid of the irritants between our two countries," said a U.S. official. Whether the price gap can be closed is not clear.

Whether it should be is also subject to debate.