The West German government announced today that the U.S. Army has completed the deployment of all 108 Pershing II missiles, which began arriving here two years ago in an atmosphere of political controversy and emotional street protests.

West German Defense Ministry officials confirmed that the U.S. 56th Field Artillery Brigade was now equipped with 36 single-warhead Pershing II missiles at each of three sites, near the towns of Mutlangen, Heilbronn and Neu-Ulm in southwestern Germany.

The Pershings have evoked angry condemnation in Moscow because they can strike Soviet territory in less than 14 minutes. While Soviet opposition remains undiminished, the massive demonstrations against the missiles that once convulsed West Germany have subsided as a sense of political exhaustion has slowed the antinuclear campaign.

The missile deliveries were halted last January after three U.S. soldiers burned to death in a fire while unloading components from a shipping container. A U.S. Army investigation concluded that a rocket motor, packed with solid fuel, ignited from static electricity and caused a flash fire. Deployment resumed only after the missiles and their transporters were modified to prevent a recurrence of the fire.

The final Pershing installments mean that the North Atlantic Treaty Organization has based 140 intermediate-range launchers in Western Europe to counter the Soviet arsenal of SS20 missiles. Britain, Italy and Belgium have already stationed 32 cruise missile launchers on their territory. Each cruise launcher carries four missiles, for a total of 128.

The United States has put forward a proposal at the Geneva arms talks that would limit medium-range missiles to 140 launchers on each side. NATO governments last week approved this offer and expressed the hope that the Soviet Union will respond when the Geneva negotiations resume in January.

The Soviet Union has indicated willingness to reach an early agreement on intermediate-range missiles by dropping its previous insistence on linking progress in that area to other negotiating forums on strategic nuclear weapons and space defense arms.

Senior West German officials said they were also heartened by signs that Moscow might be prepared to discuss short-range missiles, based near the East-West frontier in East Germany and Czechoslovakia, and to negotiate with France and Britain on their national nuclear forces to reach arms control pacts that would encompass all nuclear weapons in Europe.

Chancellor Helmut Kohl is expected to sound out U.S. Secretary of State George P. Shultz on the prospects for an interim accord on nuclear missiles deployed in Europe by both superpowers when the two men consult Saturday at Kohl's private residence in Oggersheim.

In its latest proposal to restrict both sides to 140 medium-range launchers, the United States stipulated that it wanted to retain the freedom to choose whatever mix of Pershing and cruise missiles it found most desirable. But a senior aide to Kohl stressed that the Bonn government expects to see a significant reduction in Pershing II missiles as part of any Soviet-American agreement. The Pershings may be cut back to as few as 36 missiles, which the U.S. Army considers the minimum operable force, the official said.

If the United States and the Soviet Union fail to reach an early pact curtailing nuclear missiles in Europe, the western allies have agreed under a 1979 NATO decision to proceed with further deployments of cruise missiles in five European countries, including West Germany and the Netherlands, until the full complement of 464 cruise missiles is achieved in 1988.

Besides the 108 Pershings, West Germany will base 96 cruise missiles. Britain is slated to get 160 and Italy 112 of the cruise missiles. Belgium and the Netherlands will receive 48 missiles each.

For its part, the Soviet Union has installed 441 of the triple-warhead SS20 nuclear rockets. Of these, 270 are located in the western part of the country, targeted at Western Europe, and another 171 missiles in the east are aimed at sites in Asia, according to NATO data.