After two previous unsuccessful launch attempts, the Pershing II missile yesterday completed its first flight test.

Both its rebuilt two-stage engines and advanced terminal guidance system met planned objectives, according to Pentagon officials.

"It was a good flight all the way," an Army spokesman said, "and the warhead landed within the target area" at White Sands Missile Range in New Mexico.

The launch was part of a speeded-up test schedule for the missile that is key to the North Atlantic Treaty Organization's nuclear weapons modernization in Europe. Under a program adopted in December, 1979, the first of a planned 108 Pershing II missiles are to be ready for deployment in West Germany by December, 1983.

To meet that deadline, however, the Army has been forced to begin production of Pershing II components while still testing the weapon.

Yesterday's Pershing II shot was designed primarily to test the new guidance system and so the missile was fired almost 200 miles straight up and only 66 miles down the White Sands range. But it also became the first flight test of the rebuilt, two-stage solid fuel motors that had failed during the first test firing in July.

Another short-range shot is planned at White Sands in the next few weeks before two flight tests at the missile's projected 1,000-mile range are launched from Cape Canaveral, Fla. Based on yesterday's success, a Pentagon spokesman said the remaining test schedule "looks pretty good."

Last Tuesday, a House Appropriations subcommittee cut $504 million in production funds from the administration's fiscal 1983 defense money request. The action came on an amendment by Chairman Joseph P. Addabbo (D-N.Y.), who argued that production of the missile should be delayed until testing was completed.