A leak of hot gases from a motor casing 14 seconds after ignition caused the new Pershing II missile to fail on its first flight test last month, according to an Army investigation.

Correcting the flaw in the part and installing it in a new motor will take at least two months, an Army official said yesterday. That would mean another delay in the planned second over-water 1,000-mile test for the new weapon, the future deployment of which in western Europe has become a leading issue in the current arms talks between the United States and Soviet Union.

Under the original test schedule, the second test was to take place in May.

Despite this five-month delay, Army officials maintained yesterday that neither production nor planned deployment of the missiles to West Germany in late 1983 or early 1984 will be postponed.

With their 1,000-mile range, the 108 Pershing IIs the Army plans to deploy would give NATO a weapon that could reach Soviet soil within eight minutes of firing. And combined with the 464 ground launched cruise missiles to be placed in Europe, the allies would have a force comparable to the 300 SS20 intermediate range missiles the Soviets already have in operation.

That prospect has caused the Soviets to protest deployment of the new U.S. missiles. But it has also led Moscow to join Geneva talks on limiting intermediate range nuclear systems in Europe.

The Army originally had not planned to have the Pershing II ready for deployment until December, 1984.

To meet the current date, the Army was forced to reduce planned tests from 28 to 18, with only two at the full 1,000-mile range. The service also had to begin production of the Pershing II in June, a month before the failed first flight test took place.

The investigation showed that high-pressure gas leaked through one of three supposedly sealed joints in the the rocket motor casing. In an area between the first and second stage of the missile, the high-pressure gas broke a cable to set off an automatic explosive device which destroyed the first stage and prematurely ignited the second.

The Cape Canaveral, Fla., range safety officer then destroyed the second stage because it was going off course and the guidance system and nose cone fell into the ocean.

An Army official stressed yesterday that the "failure at a joint" in the missile's first-stage motor casing was "not a basic design flaw and can be corrected."

He said, however, that the next flight test would be delayed until a new motor could be built and tested using a new production technique to prevent the leak.

That rocket will not be ready until late September, he said, and a flight test could not take place "until 30 days thereafter."

When the first Pershing II test was scheduled for July, the second was expected within the following 30 days.

Delay of the next flight until late October or early November will cause a backup in the remaining 16 flight tests, which were designed not only to test missile components but also its complex terminal guidance system.