September's index of leading indicators -- the last major economic statistic to be released before Election Day--continued to point toward a recovery, but only a weak one, the Commerce Department reported yesterday.

The index, which often foreshadows changes in economic activity, rose 0.5 percent last month as a result of surging stock prices and an increase in residential building permits. The various indicators related to jobs continued to fall.

President Reagan, campaigning in Salt Lake City, called the increase "another patch of blue," and added, "Pretty soon, even the diehard doom-peddlers will have to admit it: America is on her way back, and we will lead the way out of this worldwide recession."

The September gain in the index was the fifth in the last six months. But even so, it now stands only 4.2 percent above its low in March -- a signal that any recovery from the recession will be "relatively moderate," Commerce Secretary Malcolm Baldrige said.

Throughout the election campaign, the state of the economy and support for Reagan's economic policies have been the major issue in most House and Senate races and gubernatorial battles.

Most economists believe that the recession, which began in July, 1981, is continuing, but they also generally predict that recent substantial declines in interest rates will get a modest recovery going within the next few months.

The big gains chalked up by the stock market in recent weeks was the largest factor giving a boost to September's leading indicators and "reflects a growing belief in American business that some kind of recovery is, in fact, out there," and therefore is a positive sign, said economist Otto Eckstein of Data Resources Inc.

"But measures of production [in the index] showed a small positive change, or no change, or even a minus," he cautioned. "I don't think October was the month of the upturn. Maybe November is the month, and maybe not."

Voters will be casting their ballots next Tuesday, with both the timing and the strength of the recovery highly uncertain. The economic information they do have in hand can be summed up this way: unemployment is extraordinarily high and rising; inflation is down sharply.

The recession pushed the unemployment rate to a postwar record of 10.1 percent in September, with 11.3 million people out of work. Recent weekly figures on new claims for unemployment benefits indicate that the worst is yet to come. A number of forecasters say the jobless rate will hit 10.5 percent -- and conceivably 11 percent -- before the recovery takes hold and unemployment begins to decline.

The administration expects the economy to grow by no more than 3 or 4 percent in 1983, a recovery too slow to reduce unemployment very swiftly.

Meanwhile, inflation has come down significantly. The consumer price index rose 5 percent in the last 12 months, and at a seasonally adjusted annual rate of only 4.2 percent in the three months ended in September. In 1981, the CPI increased 9.4 percent.

The producer price index for finished goods, which rose 8 percent in the year ended in September, 1981, is up only 3.6 percent in the 12 months since.

Economists do not expect a re-ignition of inflation when the recovery begins because there is so much slack in the labor market and most businesses have ample capacity to increase production without beginning to approach their limits. At present, most forecasts for 1983 show inflation running about 6 percent or slightly less.

The gross national product already has increased for two quarters in a row, at an annual rate of 2.1 percent in the spring and at a 0.8 percent rate in the summer. However, final sales to consumers and to businesses -- as well as industrial production--all have continued to fall.

Baldrige agreed with the president's assessment that the increase in the leading indicators, and an upward revision for August, "strengthens the prospect that recovery is near."

But Baldrige went on to note in a statement that the 4.2 percent rise in the index since March is smaller than any six-month increase preceding the seven economic recoveries since World War II. The index climbed an average of 8.4 percent in those earlier half-year periods, he said.

In those recoveries, the leading indicators turned up, on average, three months before industrial production, Baldrige said.

"This time, the trend in the leading index has been upward since March and, based on past experience, recovery in industrial production is overdue. Rapid inflation and high interest rates were the problems which brought on this recession, and their recent easing has set the stage for recovery," he said.