The chairman of the president's Council of Economic Advisers said yesterday the recession will last longer than previously expected and unemployment will get worse than the Carter administration had forecast.

Charles L. Schultze predicted the inflation rate will fall below 10 percent later this year, but said he does not expect an upward swing in the economy until sometime next year.

Schultze, who appeared on "Face the Nation" (CBS, WDVM8) said the Carter administration has ruled out a quick, economy-stimulating tax cut before the November election.

But "once inflation is moving down, next year, we both deserve and need a tax cut," added Schultze. For the present, he added, the administration will pursue "a policy of fiscal tightening to deal with inflation."

Schultze said the nation's economy is "slowing at a faster rate than expected, because corrective factors are taking effect."

He said he expects double-digit inflation to end, "during the second half, maybe sometime this summer," but warned that inflation will persist in the range of 9 to 10 percent.

Slowing the rate of inflation "should reduce the erosion of purchasing power" for consumers, but also will lead to further unemployment, he ackowledged.

The jobless rate "will be somewhat higher than we had forecast -- 7 1/4 percent," Schultze added. He would not speculate on how severe unemployment might get.

Schultze echoed other complaints from the White House that lenders are not reducing interest rates fast enough, though he noted that short-term interest rates are already lower than they were a year ago.

"There is no reason why the prime rate should not continue to fall for a while," he added, and said consumers can expect "perhaps some moderate further decrease in mortgage" interest rates.

The recent decline in mortgage rates from 17 or 18 percent to about 13 percent has been a major factor in bringing down growth in the consumer price index, the top administration economist said.

There is still inflationary pressure from oil prices. Schultze added, and he said the latest increase by petroleum exporters will add 3 1/2 cents to the cost of a gallon of gas. He said the oil import fee advocated by the president also will cause a "temporary jump" in the cost of living if it is approved by Congress.