The Carter administration is proposing a new theater defense military package for the North Atlantic Treaty Organization that would trade off existing atomic hardware in Western Europe for longer-range nuclear missiles capable of reaching Soviet targets.

Introduction of the new missile - the extended-range Pershing II - is already stirring public controversy within the NATO alliance and has become a target of Soviet criticism.

U.S. officials, mindful of the alliance crisis that developed over proposed deployment last year of neutron weapons, are attempting to lay the groundwork for a December NATO ministerial meeting that would announce:

A 1,000-mile extended-range Pershing II missile will be built by the U.S. and by 1983 based in several unnamed NATO countries.

The number of nuclear systems now in Europe designed for use on NATO territory - such as artillery and atomic demolition munitions - will be reduced.

The total number of Pershing II's deployed could be limited if the Soviet Union agreed to some unclear arms limitations for European theater systems.

The NATO allies might eliminate U.S. forward-based systems - those fighter aircraft stationed in Europe, armed with nuclear bombs that could hit Soviet targets.

By reducing the number of nuclear artillery systems in Europe, U.S. negotiators hope to keep down opposition of political forces that object to nuclear weapons designed for use on West European soil. That group was particularly vocal among opponents to NATO's deploying neutron weapons.

The United States is also pushing for NATO to come up with an arms control package built around the new missile system. Such a plan would also help develop politt any NATO target, even those in Iceland.

U.S.%N THE SOVIET BUILDUP OF ITS OWN EUROPEAN NUCLEAR SYSTEMS - PARTICULARLY THE SS20, a 2,5000-mile mobile missile that carries three large nuclear warheads and can hit any NATRO target, even those in Iceland.

U.S. government officials, from the Pentagon to the Arms Control and Disarmament Agency, see the effort to gain NATO acceptance of the new missile as important in maintaining the alliance's military viability.

As one official put it, "We have to demonstrate to the Soviets that the alliance can take tough decisions." And, he added, "We will signal the Soviets that when they engage in this behavior [building up SS20s], the West can respond in a way to make them uncomfortable."

While most nuclear arms control efforts in the past 10 years have been directed at strategic weapons, both the United States and the Soviet Union have moved to modernize their more numerous theater nuclear forces.

The once overwhelming U.S. and NATO advantage in these shorter-range nuclear weapons has all but vanished in the face of increased Soviet deployments.

At a Feb. 22, 1979, closed session of the Senate Armed Services Committee, Gen. Alexander M. Haig Jr., the NATO commander, said there is "a current Soviet advantage, especially in long-range theater nuclear systems," according to the recently-released transcript.

NATO military men last year agreed that something more than the 400-mile Pershing missile was needed to meet the asymmetry caused by increased deployment of the Soviet SS20s.

The United States already had under development ground and sea-launched versions of the cruise missile. However both versions of these accurate nuclear weapons had already drawn Soviet attention and concern.

At the strategic arms limitation treaty negotiations, the Soviets insisted the range of these two cruise missiles - at least for the next three years - be limited to 360 miles, thus preventing them from being capable of reaching Russian territory from Western Europe.

U.S. weapons designers turned to the Pershing, which was not limited by SALT. The range for that ballistic missile was increased and the extended-range Pershing II was born.

Development of the system was the easiest part of the problem. Getting it accepted by the NATO countries on whose soil it would be based was to be something else again.

The West Germans, who first raised public concern over the SS20 deployments, made it known that they would base the new missile on their soil only if another continental NATO country did the same.

That was the exact position they had taken on the neutron weapons, and neither the Netherlands nor Belgium would go along.

U.S. negotiators in talks with officials of those two countries cite the differences between the neutron weapons and the proposed new Pershing missile.

Primarily the missile is designed to hit deep into enemy territory, not for use on Allied soil. In addition, it is a nuclear system deployed in response to a Soviet weapon.

At the last NATO maneuvers, use of a NATO long-range missile was played out and, for the first time in many such exercises, no nuclear devices were said to have been exploded on allied territory.

American officials hope to get both countries to accept the new missile, thus spreading the political heat that the decision is bound to create, particularly among left-wing European elements.