Productivity in the nonfarm business sector jumped at an annual rate of 2.6 percent in the third quarter of this year, the Labor Department reported yesterday.

It was the largest productivity rise in this sector for three years, and it followed a 3.7 percent decline in the three months March to June.

Major wage settlements negotiated so far this year are up over last year, according to another report issued by the Labor Department yesterday. In the third quarter of 1980 wage increases of 10.7 percent on average, excluding cost of living adjustments, were agreed for the first year of the new contract. c

First year wage increases in the major collective agreements reached between January and June 1980 averaged 9.7 percent, up from 7.4 percent in the whole of 1979, the department said.

Productivity in the private sector overall, including farming, rose by 1.4 percent in the third quarter of 1980. It was the first increase in productivity since the 0.3 percent annual rate rise in the final quarter of 1978.

The rise in the productivity of private businesses outside the farm sector resulted from a 1.1 percent rise in output and a 1.4 percent decline in hours worked, the Labor Department said.

Productivity gains are usual at this stage of the economic cycle. Output began to pick up in the third quarter of this year, as economic recovery got underway. But the number of hours worked was still falling. Hence productivity, which is the amount produced by the hour worked, rose.

However, manufacturing industry saw a further fall in its productivity in the three months June to September, as manufacturing output trailed the rest of the economy. It dropped by 10.1 percent in the quarter, measured at a seasonally adjusted annual rate. Productivity in manufacturing fell by 2.7 percent, at an annual rate, after a 4.7 percent drop in the previous quarter.

Durable good manufacturers in particular were still suffering from recession in the third quarter. Output in this sector dropped by 13.1 percent at an annual rate in the three months June to September, while hours worked fell by 9.7 percent. Measured productivity was down by 3.8 percent at an annual rate.

"It is not unusual at all for productivity to turn upward at the end of a recession because work forces, still small from recession-induced layoffs, produce more as orders for new business increase," Labor Department economist Lawrence Fulco said.

Slow or negative productivity growth has become one of the economy's most serious problems. President Carter and Ronald Reagan have promised tax cuts for business which are aimed at boosting investment and productivity. Yesterday's figures do not mean that this problem has now been solved, as it has more to do with the business cycle than with whether industry is more efficient or productive.

"I'm still looking for a decline in productivity in the fourth quarter," Sandra Shaber, senior economist with Chase Econometrics, said yesterday. Third-quarter productivity in the whole of the private business sector was 0.5 percent below the same time last year.

The major wage settlements negotiated in the first nine months of 1980 provided 7.3 percent annual average wage rises.