Six hundred and twenty-nine thousand initial claims for unemployment benefits were filed in the last week of August, the second-highest number since the recession began a year ago, the Labor Department said yesterday.

The report came as President Reagan told an audience in Kansas yesterday, "Yes, recovery has been sighted. . . . Unfortunately, unemployment is just about the last indicator to turn around after a recession."

In the past four weeks, the level of new claims has jumped by more than 100,000 as industries such as auto manufacturing have made new cuts in production. Some analysts expect the U.S. unemployment rate to climb to 10 percent or above for September from the 9.8 percent level of July and August.

Meanwhile, the Commerce Department said a survey of business investment intentions conducted in late July and August showed corporations sharply cutting plans to build new plants and buy new equipment.

After adjustment for inflation, capital spending by business will drop about 4.4 percent this year from its 1980 and 1981 levels, which were about the same, the Commerce Department said.

Including the amounts needed to cover inflation, spending was projected at $323.7 billion, up 0.7 percent from 1981. That is less than the 2.2 percent rise reported after a similar survey in the second quarter and much less than the 7.3 percent gain indicated by an initial survey taken in January and February.

Most economic forecasters believe business investment will continue to decline until some time next year, with some of them not expecting it to turn up again until the fourth quarter of 1983. A number think this year's drop will end up larger in real terms than the 4.4 percent figure shown by the survey.

The spending cutbacks are the result of extremely low use of existing production capacity -- which may have hit a postwar low in August -- poor profitability, high interest rates and unusual difficulties for many companies in borrowing on a long-term basis. If long-term interest rates continue to fall, the turnaround in investment could come sooner than now predicted, analysts said.

According to the survey, every major industry group plans to reduce investment this year in real terms, with manufacturers' spending falling 6.6 percent and that of nonmanufacturers by 3.1 percent.

Commerce Secretary Malcolm Baldrige noted that the latest survey was taken before August's interest rate declines.

President Reagan, speaking at the University of Kansas, disclaimed responsibility for either the recession or the high level of unemployment. "The . . . problem is, unemployment has been gaining on us for years," he declared.

"Since 1976, the unemployment rate in this country averaged over 7 percent, far higher than in earlier postwar years," he said. "High inflation and interest rates pushed more and more families to seek a second income. To charge that our administration is trying to reduce inflation on the backs of the unemployed is to stand truth on its head.

"More than anything else, it was those record interest rates and double-digit inflation that led inevitably to the recession. And that's what we're trying to hard to turn around," Reagan said.