The next flight test of the troubled Pershing II missile has been delayed several weeks until early September while the test rocket's engines are returned to its manufacturer for X-ray examination, Army sources said yesterday.

In 16 previous flight tests of the Pershing II, which is to be deployed with nuclear warheads in West Germany beginning in December, the missile exploded twice, failed to operate properly two other times and badly missed its target in a fifth test.

Another test failure, so close to its planned initial deployment, could create political as well as technical problems for the Pershing II, according to the sources. They said any delay in deployment would give western European opponents of the medium-range nuclear weapon more time to try to block it.

The next Pershing II to be tested, like the one that failed last month, has been subjected by the Army to several months of field tests, in which troops at Fort Sill, Okla., moved it around and practiced countdowns without firing the missile.

One source said the Army wants to "check the motors over very carefully" to determine if the "jiggling and vibrations in the field" have had any effect on the motors.

X-ray examination has "not been done before" in the Pershing II program, the source said, but failures in three of the last four test shots have made the Army and the missile contractor, Martin-Marietta Co., especially cautious in preparing what was to be the next-to-the-last flight test of the missile.

Last month's flight test failure was blamed by the Army on a cast-iron ring that was out of position, permitting pressure to blow open a circular plate and destroy the complex $2 million missile.

An Army spokesman said yesterday that it was not known why the ring was out of position in that test.

The new delay will prevent completion of the Pershing II test flights this month, as once planned.

Originally, the tests were to have been completed in May.

One source said that both the Army and the manufacturer "had been talking about doing even more development testing," and "if we lose one of the next two, would certainly do more testing."

Earlier this month, Army Undersecretary James R. Ambrose, speaking of the problems with the Pershing II, told reporters that "we will not deploy this kind of weapon" until the probablility of its success under combat conditions is between "80 and 90 percent."

Last week, however, Defense Secretary Caspar W. Weinberger said that deployment will begin as planned in December despite the testing problems.

A Pentagon spokesman said yesterday that officials are "certain" that they will meet the deployment deadline.

Under a 1979 agreement among the NATO allies, the first nine Pershing II missiles are to be deployed in West Germany while 16 ground-launched cruise missiles are scheduled to be deployed in Britain in December.

Another 16 cruise missiles are to be put in Italy at the same time, though some military sources have said that their base in Sicily may not be ready by December.

Despite the flight test problems, the first five Pershing II production models already have been delivered to the Army, a spokesman said yesterday.

The Pershing II is being tested and produced concurrently to meet the deployment deadline.

The Pershing II, which could hit targets in the Soviet Union within 10 minutes of its launch from West Germany, has been strongly opposed by Moscow and anti-nuclear groups in western Europe.

Altogether, 108 U.S. Pershing II missiles are to be deployed in West Germany, and 464 slower, ground-launched cruise missiles are to be deployed in Britain, Italy, Belgium, The Netherlands and West Germany.

In Intermediate Nuclear Force negotiations with the Soviet Union at Geneva, the United States has offered to limit its deployment of these missles if the Soviets reduce or eliminate all of their medium-range, SS20 nuclear missiles targeted on western Europe.