Influential Algerians are convinced that the Reagan administration has muffed the United States' best chance for improving political relations with Algeria since this pivotal North African nation fought its way to independence from France in 1962.

Less than two months after praising Algeria profusely for helping negotiate the American hostages' release from Tehran, the United States in rapid succession has angered Algeria by:

Approving tank sales to Morocco.

Ending negotiations for a billion-dollar-a-year liquefied natural gas deal.

Delaying action on such pet Algerian and Third World concerns as the Law of the Sea draft treaty.

Aside from a few inspired newspaper comments, Algeria has refrained from official public condemnation of these American decisions, apparently preferring to write them off as teething problems of a new administration. But as an influential editor here noted privately, "We have sufficient reasons to be furious" over what politically minded Algerians look on as slaps in the face.

European diplomats in Algiers described the Reagan administration's actions as disturbing in substance and clumsy in timing.

The Algerian goverment's discretion reflects a tradition of diffidence -- mixed with an occasional smattering of arrogance -- and a system of priorities attuned to the Third World that has never set much political store by the United States.

"The hostages were not merchandise delivered to the United States with a price tag attached," a Foreign Ministry official said.

Nonetheless, Algerian officials are aware of the groundswell of sympathy and thanks their role evoked in the United States where, as one Algerian journalist noted, "for the first time the American people knew we existed and were not to be confused with Nigeria, Liberia, Bulgaria or one of those distant countries ending in ia."

But Washington behavior since then, officials have noted, seems to underscore an Algerian impression that the United States views policy through a superpower prism in which the Third World causes that Algeria likes to champion have little place.

Whether or not the Reagan administration intended it that way, the timing of recent developments drove home this impression with renewed intensity.

Within a week of the inauguration and hostage release, the administration announced plans to sell Morocco 108 M60A3 tanks, despite Algerian backing for the Polisariio forces who have been fighting the Moroccan Army over the disputed Western Sahara.

Adding insult to injury in local eyes was the administration's unadorned support for Morocco in apparent keeping with its new policy of aiding "friends."

Unlike the Carter administration's 1979 sales of F5 jet fighters over OV10 Bronco observation aircraft to Morocco, Reagan's team dropped language justifying the decision as a way to facilitate a peaceful settlement of the Sahara conflict. Algerian officials were not fooled even then, but they noted the omission this time.

By way of explanation, Algerian officials were told that the United States would have announced the tank deal earlier had it not been for the then unresolved hostage crisis in Tehran.

"Who knows? Maybe that was true in the American context, although the reasoning is pretty unfeeling," an observer noted. "But you couldn't find a single Algerian who would believe it."

The Algerian Foreign Ministry officially protested the arms sale, and the next day exiting Ambassador Ulrich Haynes said he hoped the United States would adopt a truly neutral stance on the Sahara.

But on the aftermath of the hostage crisis, the Algerians have sworn themselves to complete silence. Algeria now refuses even to acknowledge suggestions that the United States has failed to honor various aspects of the release deal's complicated provisions.

This stance is part of the Algerians' contention that their role was purely humanitarian, intended to help Iran salvage its revolution and in no way designed to curry favor with the United States.

To have hoped for special consideration after the hostage release was nevertheless only human.

But on Feb. 18, U.S. negotiators arrived from Washington with a take-it-or-leave-it proposal for the liquefied natural gas deal. Specialists said the terms were less generous than those previously than those previously proposed and Algeria rejected them. The government-controlled media accused the United States if bad faith and using "unilateral rupture" of the negotiations to broadcast Reagan's hard-line approach on foreign policy.

Specifically at stake in the complicated negotiations were Algerian efforts to force the United States to accept that gas and oil should be sold at the same price per calorie and American fears that such a concession would trigger price leapfrogging by Canada, the principal foreign source of natural gas used in the United States.

The upshot of the breakdown was that Algeria had no immediate customers for its $2.5 billion worth of wells, pipelines and liquefaction plants. Its putative American partner, El Paso, wrote off $375 million for 1980 alone in gas tankers. East Coast customers of companies that spent $700 million on regasification plants will be paying for them for the foreseeable future in their monthly bills.

During six negotiating rounds under the Carter administration the United States had "been willing to pay more, but not much more," an analyst said. Observers here noted an expectation that the Reagan administration would be forthcoming since it deregulated -- and thus increased -- domestic oil prices that figure in complicated natural gas price calculations.

But as seen here, the Reagan administration is in no frame of mind to give presents to prickly, if occasionally useful, countries like Algeria. Ever since the Vietnam war, that is the way many Algerian leaders prefer to see American policy, no matter how sterotyped such analysis may appear to outsiders.

A prominent Algerian editor who had just finished former president Richard Nixon's memoirs said he supposed Reagan "was going to try to carry out the hard-line, anti-Soviet, to-hell-with-the-Third-World policies which Watergate and the Vietnam debacle prevented" his Republican predecessor from pursuing.

About the only pending piece of bilateral business involves possible sale of U.S. C130 military transport planes. Algeria earlier acquired some L100 civilain versions for its commercial airline, Air Algerie. But it has been unable to buy C130s because of a U.S. ban on military sales to the Algiers government, with which foreign-policy disagreements.