The Labor Department said yesterday that its employment cost index, a measure of labor costs for employers, rose only 3 percent in the past year for private industry workers, the lowest such increase since the index was established 11 years ago.

With labor costs for state and local governments rising somewhat faster than in the private sector, the overall employment cost index increased 3.3 percent in the year ended in June. Federal, farm and household workers are not covered by the index.

The index, regarded by many economists as the best available measure of trends in labor costs, is calculated on a quarterly basis. It includes wages, salaries and the cost of fringe benefits provided by employers, including those required by law, such as Social Security and worker's compensation.

In every major part of the index, the increases in the past year were smaller than in the year ended in June 1986.

For instance, the 3.3 percent increase in the overall index was down from 4 percent the previous year. The 3 percent figure for private industry workers compared with 3.7 percent a year earlier.

A number of economists have been surprised that the index has continued to show a deceleration of increases in labor costs in the face of an unemployment rate that has dropped a full percentage point in the past year. As long as labor cost increases do not accelerate, inflation is likely to remain moderate, the analysts said.

The department said the increases in several other parts of the index were also record lows: white-collar occupations, 3.3 percent; nonunion occupations, 3.3 percent; manufacturing, 2.4 percent; goods-producing industries, 2.3 percent, and the western region of the country, 1.7 percent.

Employer costs for government workers went up 5 percent compared to 5.7 percent in the previous year. For white-collar occupations, the costs went up 3.3 percent, compared to 4.5 percent, and for blue-collar workers, the increase was 2.3 percent, compared with 2.8 percent.

However, the gain for private industry service workers was 3 percent, up slightly from a 2.9 percent gain the previous year.

In a separate report, the department said major collective bargaining settlements reached in private industry during the first six months of this year called for wage increases averaging 2.1 percent in the first year of the contract and 2.5 percent annually over its life.

The 225 contracts covered 732,000 workers. The last time the contracts were negotiated, generally two or three years ago, the first-year increases averaged 1.7 percent and 2.6 percent annually over the contracts' term.

Settlements in manufacturing, in which many industries face strong competitive pressure from foreign producers, averaged a scant 0.2 percent for the first year and 0.9 percent annually over the life of the contracts. Slightly more than 200,000 manufacturing workers were involved.

Gains were larger in nonmanufacturing industries, averaging 2.9 percent in the first year and 3.1 percent annually over the entire contract.

About half of these workers, 269,000, were in construction, and their increases were just a bit higher, 3 percent and 3.2 percent respectively.