The productivity of American workers rose slightly last quarter for the first time in 15 months, but analysts said the improvement was limited and didn't represent a full turnaround of the past year's dramatic decline.

Labor Department figures showed output per work hour edged up at an 0.6 percent annual rate between January and March after declining at an 0.3 percent pace the previous quarter. It was the first actual rise since late 1978.

However, the gain came entirely in the volatile farm sector. Productivity in the rest of the economy dipped at an 0.2 percent annual rate, following an annual rate of increase of 0.7 percent during the previous quarter.

As a result, the average unit labor costs of American business soared at a 10 percent annual rate, heightening pressures on companies to increase their prices. Unit labor costs rose at a 7.8 percent pace the previous quarter.

At the same time, the department reported that the average first-year wage increases in major collective bargaining settlements in the United States accelerated to 7.8 percent last quarter from a 7.4 percent average for 1979.

The speedup, albeit troublesome to some economists, nevertheless was considered moderate in the face of the current 18.2 percent inflation rate. The average wage boost over the lives of the contracts involved was 6.3 percent.

Yesterday's reports did little to alter previous trends either in wage increases or productivity. The decline in productivity has been stabilizing gradually over the past two quarters, while increases in unit labor costs have slowed.

Nevertheless, William A. Cox, the Commerce Department's deputy chief economist, cautioned that productivity may decline in upcoming quarters in part because the economy is entering a recession.

The performance of productivity is important to the nation's ability to dampen inflation because, without gains in output per work hour, business cannot absorb higher wage costs easily without raising prices.

Economists have not been able to agree on precisely what is causing the falloff in productivity. Explanations range from a lack of adequate investment to a shift away from manufacturing and more toward services.

The restraint reflected in the figures on major collective bargaining settlements was encouraging to administration economists. The White House has feared the price surge might spill over into wages.

The reports yesterday came as Citibank, the nation's second largest, joined other major U.S. banks in reducing its prime lending rate to 19 1/2 percent from 20 percent -- a move the others took last Friday.

Earlier this week, Chase Manhattan Bank lowered its prime to 19 percent, and promptly was followed by several other large banks. The prime is the interest rate banks charge their most creditworthy corporate customers.

As has been the case for the past several quarters, productivity performance varied widely among key sectors of the economy in the January-March period. Output per work-hour in manufacturing fell at an annual rate of 1.9 percent.

The rise in overall productivity for the private business sector reflected a 1.1 percent gain in output during the period and an 0.5 percent increase in total number of hours worked.