The first flight test of the controversial Pershing II missile, which had been set for yesterday, has been postponed until early July, according to informed sources.

But because of pressure to meet the NATO deployment schedule, the Army has been given the go-ahead to begin production of the new weapon system before all its flight testing is completed.

NATO allies were recently told "there have been delays in schedules," according to one diplomat, but they were assured that would not affect deployment dates.

"The Pershing is so bound up in NATO politics and arms control negotiations," one congressional defense expert said yesterday, "that we could end up deploying a system that doesn't work."

The NATO decision to begin deploying both the Pershing II and ground launched cruise missiles is expected to be discussed at the summit meeting President Reagan is attending in Bonn next week.

The Pershing II, whose warheads would be able to hit Soviet targets within 10 minutes flight time from NATO bases in West Germany, has become a flash point in the arms race between the United States and Soviet Union, drawing particular criticism from Russian leaders and protests from antinuclear groups in NATO countries.

The original date for the first Pershing II test was in April. Last fall, however, the Army said it would be pushed back to June 2. Now it is scheduled for "early July," according to an official involved with the system.

The first two flight tests of the Pershing II, to take place at Cape Canaveral, Fla., are important because they are the only ones in the 18-test flight series in which the missile will be fired over water to its planned 1,000-mile range.

The remaining tests will travel only 600 miles over land, probably from Idaho to White Sands Missile Range, N.M.

Last year, Army witnesses told Congress that a production decision on the Pershing II, called a DSARC III in Pentagonese, would be held this month, after the first two flight tests had been completed and reviewed.

Yesterday, however, an Army spokesman confirmed that Defense Secretary Caspar W. Weinberger actually "gave a production go-ahead last November." The DSARC III, he said, now is scheduled for November, but is being called a "production continuation decision."

Under NATO's deployment approval of December, 1979, the first batteries of the planned 108 Pershing II missiles were to be placed in West Germany in December, 1983, or early 1984.

The Army, which is developing the system, has had problems meeting that schedule. When it first proposed building a Pershing II in the mid-1970s, the plan was to have it ready for deployment in December, 1984. That date was moved up at the time of the NATO decision, but the Army has found building the missile more difficult and costly than expected.

The cost of a battery of nine Pershing IIs rose $61 million, to $168.7 million, between March and December last year, according to a recent report to Congress by Army Secretary John O. Marsh Jr.

The House Appropriations subcommittee on defense has been particularly critical of the decision to push ahead with production of the Pershing II before all its flight tests were completed. Under last years's schedule, the original 28-test program was not scheduled to be completed until August, 1983, just four to six months before the first missiles were scheduled to be operational in West Germany.

The new "compressed test schedule," as the Army spokemen call it, will be completed earlier, but still well after full production of the missiles will be under way.