The United States has proposed at the Strategic Arms Reduction Talks in Geneva that the Soviet Union make much bigger cuts in its long-range nuclear missile forces than the Reagan administration has indicated publicly, administration officials revealed yesterday.

The officials said the U.S. proposal at the START negotiations would require Moscow to scrap roughly two-thirds of its biggest and most powerful missiles and more than 70 percent of all its multiple-warhead missiles.

President Reagan and top administration officials have described the U.S. proposal, made in Geneva last June, as calling for each side to reduce its existing force of intercontinental-range ballistic missiles to a maximum of 850. The implication was that each superpower could decide what kinds of missiles to keep within that limit.

But officials said yesterday that in the opening round of the talks last summer the United States proposed so-called "collateral constraints" designed to force sharp reductions in the most threatening class of Soviet missiles, those theoretically capable of knocking out U.S. land-based missiles in a first strike. These proposals call for the Soviet Union to reduce their current force of 788 SS17, SS18 and SS19 multiple-warhead, land-based missiles to a maximum of 210.

Of those 210, a maximum of 110 could be SS18s, the largest missiles in the Soviet arsenal. The Soviets have 308 of these supermissiles, each of which can carry up to 10 atomic warheads.

The Soviets also have 330 SS19s that can carry up to six warheads and 150 SS17s equipped with four warheads each. The SS17s and SS19s are classified as "medium-weight" missiles and the SS18s as heavy-weights.

They all are several times more powerful than the existing U.S. Minuteman missiles, some of which carry three warheads and which are classifed as "light" missiles in negotiating terminology.

U.S. officials acknowledged that the additional restrictions proposed by the Reagan administration will make a START agreement even harder to reach.

But they say it is important to remove fears of a Soviet first strike, which drives the arms race here.

They said the 210-missile limit was chosen because that would allow the United States to deploy a roughly similar number of new 10-warhead MX "medium" missiles. If the United States deployed more than 210 MX missiles, the officials said, the Soviets could claim with some validity that the United States was building a first-strike force of its own.

A special commission appointed by Reagan recommended this week that only 100 MX missiles be deployed. But its report specifically left open the possibility that more could be added if the arms control negotiations are unsuccessful. The United States also proposed last year that each side agree to equal levels of long-range bombers.

The United States specified that the Soviet "Backfire" bomber, which Moscow has contended is not an intercontinental-range weapon, be counted as a strategic bomber able to attack the United States. In the most recent round completed in March, the United States proposed 400 bombers on each side.

Initial reports of the "collateral constraints" proposed by the United States in Geneva appeared in Time magazine.

At the moment, the Soviet Union, according to U.S. figures, has 1,398 land-based ICBMs and 950 submarine-launched ballistic missiles, while the United States has 1,000 land-based Minuteman missiles, 43 Titan ICBMs and 568 submarine-launched ballistic missiles. Both sides have about 7,500 atomic warheads on those missiles, and Reagan's original START proposal made last June calls for each to reduce its warheads to 5,000 on no more than 850 missiles.

U.S. officials acknowledged that there is virtually no chance that Moscow will accept the U.S. proposals as they stand.

They also acknowledged that there is not likely to be any progress toward compromise in the START negotiations until the question of intermediate-range nuclear missiles based in Europe is resolved in companion negotiations in Geneva. The United States would seek to eliminate all remaining SS18 heavy missiles in a second phase of START.