The recession has virtually bottomed out, unemployment is near its peak and double-digit inflation appears to be at an end, the chairman of the president's Council of Economic Advisers said yesterday.

"I think the recession is just about at its bottom," presidential adviser Murray L. Weidenbaum said. "I think the next turn in the economy clearly will be upward. We already have some modest signs of that."

Appearing on the CBS program, "Face the Nation" (WDVM-9), Weidenbaum said the administration has made "extraordinary progress" in bringing down inflation. He said the progress began before the recession, "as soon as we shifted away from the unsustainably rapid growth in the money supply."

He said the double-digit inflation "that characterized the economy when this administration took office is behind us and will stay behind us as long as the monetary fiscal restraint effort continues."

Weidenbaum repeated his belief that the unemployment rate will peak around 9 percent, then start to decline.

Asked if that is likely to occur soon, he pointed out that unemployment typically lags other indicators, beginning to fall after an upturn in the economy, and he predicted "an increase in the size of that upturn in the second quarter."

That does not mean, however, that the recovery will be quick and painless, he said. "Many business firms are learning that a less inflationary environment is perhaps more painful to adjust to than they realize. It's a healthy, necessary kind of adjustment."

While acknowledging that millions remain unemployed, he asserted: "I don't want to lose sight of the 99.6 million people who are employed and who are benefiting from a lower inflation tax on their income and their savings."

He said he expects "an increasing array" of new jobs to be created in the economy, but strongly rejected a suggestion that the federal government should attempt, for example, to ease serious unemployment brought on by problems in the hard-hit auto industry.

He said the administration's three-phase tax cut is an essential part of a program to increase economic growth and create millions of jobs. And he insisted that there should be no "tampering" with the third installment of the tax cut in an attempt to reduce government spending and the budget deficit.