In its attempt to reshape the American-Soviet strategic balance, the Reagan administration--barely beginning to find its own center of gravity after 16 months in office--has taken on what would be a formidable test for the diplomatic and political skill of the most finely tuned American government.

At a time when Soviet leadership is approaching the end of the Leonid Brezhnev era and is least receptive to innovations in the superpower balance, the United States is seeking drastic reductions in the weapons the Soviet Union prizes the most.

Western equilibrium simultaneously is in poor position for bold attempts to change the strategic balance. To sustain its new arms control venture, the Reagan administration requires an exceptional level of American News Analysis News Analysis consensus and allied support, just when soul-searching discord about nuclear weapons and doctrine is at a 25-year peak in the western alliance.

President Reagan's new negotiating offer gives his administration and allied governments a welcome measure of relief from this ferment. That was one of its objectives. The Soviet Union, which has enjoyed the emotional high ground in Europe by calling for urgent resumption of negotiations on strategic nuclear weapons, is intent on making that breathing spell as brief as possible.

Bargaining and posturing on strategic nuclear weapons rebounds across the full range of superpower competition. "Every judgment we make," Secretary of State Alexander M. Haig Jr. said recently, "and every judgment the Soviet leadership makes" is "shaded by" the "state of the strategic balance."

What is at stake now is more out in the open than is usually the case in pre-negotiation maneuvering over limits on strategic weapons. Over the opposition of some specialists who wanted an even tougher bargaining position, the Reagan administration is committed to negotiations which in the president's words are aimed at "the most dangerous and destabilizing" weapons--notably "land-based" intercontinental weapons.

The meaning of the numbers and categories of weapons to be reduced is unmistakable to the Soviet Union: The U.S. formula for reducing the nuclear threat would wipe out the Soviet Union's advantage in more powerful land-based intercontinental missiles with multiple warheads, the core of the Soviet strategic force. The Soviet Union has nearly three-quarters of its strategic power in these land missiles, while less than one-fourth of American intercontinental missiles are land based. The bulk of the American strength is in submarine-launched missiles and strategic weapons carried by bombers.

Under the American plan, the Soviet advantage of about 5,500 warheads on land-based missiles--compared to 2,150 for the United States--would be eliminated. Each nations' total number of warheads on intercontinental land and sea missiles would be reduced one-third, from about 7,500 to 5,000 weapons. In addition, the number of intercontinental land and sea missiles on each side, which carry the warheads, would be reduced to about one-half of the current U.S. level, or 850 missiles. The entire cutback process would stretch over five to 10 years.

The Reagan administration has what it regards as a convincing rationale for seeking an admittedly disproportionate cut in the numbers of Soviet land-based missiles. It is that the super-powerful Soviet weapons are more provocative, and also likelier to be fired in haste than less-vulnerable sea-based or air-launched weapons.

Whether the negotiations will even reach the "first phase" in the form the United States is projecting is an open question. There are no counter-concessions yet visible on the American side other than Reagan's general statement last Thursday that "nothing is excluded" from negotiations, including bombers, cruise missiles or other weapons systems in which the United States holds an advantage.

Broadly speaking, the United States is trying to trade off some of the strength of new weapons it could produce against weapons that the Soviet Union has in place.

In the past, this kind of posture virtually would have guaranteed a preemptory rejection of what the Soviet Union would scorn as a lopsided offer. That is what happened in March, 1977, when Brezhnev and his colleagues rejected out of hand a less-demanding call from the Carter administration for deep cuts in nuclear forces.

Specialists on both sides can see many reasons that the Soviet Union has not followed a similar course this time.

For one thing, the Soviet Union does want limits on American weapons to control technological competition that could surpass it. The Kremlin also knows that some Reagan supporters would prefer no arms limitations at all with the Soviet Union. Before taking office, Reagan rejected as "fatally flawed" the proposed strategic arms limitation treaty known as SALT II, the product of seven years of tortuous negotiation, and he served notice that he would confront the Soviet Union with "the possibility of an arms race" to compel the Soviet Union to bargain on terms the United States regards as equitable.

That is not language that any administration official now employs in public, as the United States pursues a major military expansion. The Soviet Union recognizes that the United States, with an economy nearly twice as large as its own, can outspend it in an all-out arms race--if the American people are prepared to make the sacrifices that would impose.

To thwart U.S. policy, the Soviet Union counts heavily on exploiting Western Europe's deep apprehensions about nuclear warfare, to which the Reagan administration unwittingly contributed in its first stumbling months in office. Administration policy makers who scoffed initially at the Soviet portrayal of "the American threat to Europe" learned that was a potent issue, capitalizing on genuine alarm about the competency and direction of American strategy.

Soviet strategists are now bound to try to block the Reagan administration again with variations on the same theme. A centerpiece in that struggle is already discernible. It is the threat that resides in the most advanced American nuclear technology, the controversial MX land-based intercontinental missiles, and the newly developing Trident D5 intercontinental submarine-launched missiles.

Both of these weapons would be accurate enough to knock out Soviet land-based missiles, reversing the American "window of vulnerability" to Soviet attack that the Reagan administration concentrated on to help justify the expansion of American military power. With the United States armed with both the MX and Trident D5 missiles, Soviet strategic forces--the bulk of which are based on land--could be far more vulnerable to attack than American forces theoretically are now.

It is this potential American threat to the Soviet Union, however, that holds one prospect for a possible compromise to reduce the nuclear arsenals of both nations.

The MX missile, for which no basing system has yet been agreed upon, logically could be used in a trade-off with the Soviet Union in exchange for changes in the strategic balance that benefit the United States. That could still leave the United States free to deploy the latest sea-based Trident missile. No Reagan planner, however, will say at this point whether such an outcome is being given active consideration.

For years many western strategists have maintained that the only way to reduce the danger of hair-trigger nuclear war is to shift all the intercontinental weapons of both superpowers to the sea. Soviet military tradition, however, and vast expenditures, with great strain on Soviet resources, are embedded in overwhelming reliance on land forces.

Whatever American planners may envision may be totally irrelevant in Soviet perspective. There is no indication that Brezhnev, in precarious health at the age of 75, or his equally elderly colleagues, have any interest in considering any fundamental changes in the structure of Soviet forces.

Although a new Soviet initiative is believed to be imminent to counter the Reagan proposal, it is expected to be a variation on the SALT II negotiating formula. Reagan on Thursday again rejected calls from many Democrats, and from former secretary of state Henry A. Kissinger, to accept modifications in the SALT II format until a broader strategic arms treaty can be negotiated.

The Soviet Union holds the United States responsible for defaulting on three intended treaties in a row: The 1979 SALT II pact, the Threshhold Test Ban Treaty signed in 1974 to limit the size of nuclear test explosions, and the Underground Nuclear Explosions for Peaceful Purposes, negotiated in 1976, which includes the first U.S.-Soviet agreement on any rules permitting inspection of sites for nuclear explosions.

On this record, Soviet diplomats express confidence that their nation will play the role of most aggrieved party in the the contest for world opinion that will surround new negotiations on strategic weapons. That is a stance that the Reagan administration is now determined to try to reverse, to strengthen its own bargaining hand, in what is inescapably a competition in public imagery as much as it is a struggle over the weapons of nuclear war.