Productivity in nonfarm private businesses fell at a 2.9 percent annual rate in the second quarter, less than the 4.1 percent rate originally reported, the Labor Department said yesterday.

The revised figures show that output dropped at an 11.5 percent rate instead of the 12.8 percent rate first reported, while hours worked declined at an 8.8 percent rate instead of 9.1 percent.

But even with the changes, productivity performance in the quarter was extraordinarily poor. The drop in productivity combined with a sharp rise in compensation paid workers pushed unit labor costs up at a 14.1 percent rate, the department said. Increases in unit labor costs normally are reflected in higher prices.

The first figures available for the second quarter covering nonfinancial corporations -- all corporations except banks, stock and insurance companies -- showed a 1.1 percent rate of decline, the sixth consecutive quarterly drop. There were seven consecutive drops in 1973-74, the only longer period since this statistical series was begun in 1958, the department said.

Output of these corporations fell at a 10.7 percent rate in the quarter, the largest quarterly decline ever recorded.

Separately, the department said employe compensation rates rose 2.3 percent in the second quarter according to its employment cost index, with pay and benefits for blue collar workers rising slightly faster than for white collar workers.