Seventeen seconds into yesterday's first full test flight of the Pershing II, the Army's new missile that is designed to be able to fire nuclear warheads into the Soviet Union from western Europe, its first stage "malfunctioned and the missile destroyed itself."

No one was hurt, said an Army spokesman at Cape Canaveral, where parts of the missile rained down on an unpopulated area on the Florida missile test range less than a minute after its 10:50 a.m. launch.

"We're disappointed," the spokesman added, "but it is too early to tell what the impact will be." A second test was scheduled to take place within a month, but an Army official said the missile would "not be fired again until the cause is determined."

Col. William J. Fiorentino, the Army's Pershing II program manager, told reporters at Cape Canaveral yesterday that "it could be something fundamental and cause a delay of a month or more, or it could be simple and fixed in days."

Although test failures are relatively common early in the development of a new missile or warplane, any delay in the Pershing program could have significant diplomatic if not military consequences.

NATO's 1979 decision to deploy 108 Pershing IIs in West Germany--plus 464 ground-launched cruise missiles there and in England, Italy and possibly Belgium and Holland--has been the focus of strong Soviet criticism and widespread opposition from anti-nuclear groups in Western Europe. Deployment of the missiles also is at issue in the intermediate range nuclear missile negotiations now under way between the United States and the Soviet Union in Geneva.

Both the Pershing and Cruise programs have been plagued with development problems and sharply rising costs, caused in part by an acceleration of their development and production by the Army's Missile Command and Martin-Marietta to begin deployment by December, 1983, a year earlier than originally intended.

Last February, in a special report on cruise missiles, the General Accounting office found their reliability "deficient," based on the tests to date.

For Pershing, the Army had compressed the original program of 28 tests to 18, only two of which would cover the missile's full, 1,000-mile range. Today's first test was delayed from April, and then from June. Last month, the Army last month signed a production contract without flight test data.

"Any slippage of more than a few weeks," a western European diplomatic source said yesterday, "could create uncertainty whether the deployment actually will take place." This source added, however, "that setbacks such as yesterday are to be expected in program such as this."

With its planned range of 1,000 miles, the Pershing II would be able to hit targets in the Soviet Union less than 10 minutes after launch, a time span considered much too short for any Russian missile defense system. In addition, the Pershing II missile is scheduled to have a new, radar terminal guidance system which is advertised by Army spokesmen as providing "pinpoint accuracy."

After at least one more flight test from Cape Canaveral at the missile's planned extended range of 1,000 miles, there are to be 15 tests at a range of about 600 miles over land from Idaho to New Mexico. These will provide an opportunity to test the missile's unique guidance system.

That system requires a radar picture of the target area to be implanted in the missile's "brain." Then as the missile re-enters the earth's atmosphere and approaches the target, the "brain" takes a radar picture of what it is approaching. By correlating the real and stored radar pictures, the missile supposedly will achieve its "pinpoint accuracy."

To make the system work, however, the Army has to have extremely detailed radar maps of the Soviet Union and eastern Europe for initial storage in the Pershing II's brain. The Defense Mapping Agency, according to recent congressional testimony, has not been able to gather enough material to permit the type of flexible targeting the Army hoped for. Thus the first missiles deployed will have only a few fixed targets at which each can be aimed.