The long-awaited recovery has begun, but will be the weakest in post-war history, the National Association of Business Economists said in a forecast released yesterday.

The NABE's quarterly survey of 200 economists from the manufacturing, services, financial and trade sectors presents an outlook more pessimistic than those of the Reagan administration and some academics, but less bleak than those of some private economic consultants.

For example, the NABE projects real economic growth of 2.2 percent during the current quarter and 3.1 percent in the fourth quarter. That is less than half the growth rate forecast by the government. Real gross national product will increase by 3.4 percent next year, the NABE says, while Evans Economics, a Washington consulting firm, projects real GNP growth of just 1.8 percent.

The NABE sees an end-of-year unemployment rate of 9.5 percent compared with the administration's prediction of 9.l percent.

The business group is somewhat more sanguine about inflation than the administration, predicting a rate of about 6 percent for the next decade compared with the government's average of 6.3 percent over the 1981-87 period.

The business group's expectations for fourth-quarter housing starts--1.1 million on an annual basis--and new car sales--8.3 million on an annual basis--are in line with those of another leading forecaster, Data Resources Inc. of Boston.

The NABE is more optimistic about business investment in plants and equipment--foreseeing a rise of 5.2 percent next year--than is Townsend-Greenspan & Co. of New York, which looks for a continued drop until 1984.

The survey was conducted in early August. NABE President Don R. Conlan said yesterday that the recent drop in interest rates and market boom would make the macroeconomics projections a bit more optimistic, but would not affect the "guts" of the survey: current business conditions.

Coming out of the second quarter, during which profits dropped 18 percent from their level in the same quarter of 1981, the economists' businesses experienced a "slight" increase in demand, although prices still were slowing or even declining.