The Army test program for the Pershing II missile has been delayed again, the Pentagon announced yesterday.

A shot planned for this month at the White Sands, N.M., missile range has been postponed until January, the Pentagon statement said.

The postponement did not arise from a problem associated with the missile's performance, sources said, but from a potential safety problem. During the last shot, on Nov. 19, which went 200 miles almost straight up and only 66 miles down range, the second-stage motor almost dropped outside the perimeter of the missile range.

At least four test shots were unsuccessful or have been delayed in the already tight test program for the Pershing II, a 1,000-mile-range missile that is the heart of the NATO nuclear modernization program.

The missile also is the key weapon in the intermediate-range nuclear arms reduction negotiations between the United States and the Soviet Union. Soviet leader Yuri V. Andropov focused on the Pershing in his Tuesday speech on disarmament.

The first nine of a planned 108 Pershing II missiles are scheduled to be deployed to West Germany next December or early in 1984.

This most recent testing delay makes that goal even more difficult, but the Army said yesterday it will "still make the deployment date."

The Pershing's first test flight failed when the missile exploded seven seconds after launch.

Its second launch was twice postponed and finally took place on Nov. 19. On that shot, although the engines worked properly, the guidance system failed to perform as expected.

Technicians, according to Army sources, are trying to fix the missile's second-stage motor so that it will fall within the test area and not endanger nearby civilian areas.