Lester C. Thurow, a noted Democratic economist, criticized the Reagan administration and the Federal Reserve Board yesterday for their tight monetary policies, which, he charged, were keeping interest rates dangerously high.

"I think the economy is in very weak shape at the moment and another year or two of current interest rates and we will really push it off the economic cliff," Thurow warned on CBS's Face the Nation.

Drawing numerous parallels between 1929, the start of the Depression, and today--including corporate bankruptcies, bank closings, and a declining GNP--Thurow called for a quick and dramatic change in Federal Reserve policy.

Disagreeing with the Federal Reserve Board's Chairman, Paul A. Volcker, Thurow said that the agency could ease its monetary policy without renewing inflation. Short-term interest rates must be brought down, Thurow added, if the economy is to improve.

"At the moment, we need a dramatic change in interest rates," said Thurow, a professor of economics at the Massachusetts Institute of Technology. Reducing the budget deficit will not help the economy in the short run, but only in the coming years as Reagan sharply increases the budget for defense, he said.

Despite his gloomy assessment of the current economy, Thurow predicted a "little bit of an uptick after July" as a result of the $33 billion tax cut and the $7 billion increase in Social Security benefits.

"With an extra $40 billion to spend . . . Americans are going to spend and that has to help the economy . . . a little bit for a while going into the fall," he said.

However, he noted, although statisticians will be able to see some improvement in the economy late this summer, "the man on the street won't see anything get better until Thanksgiving, Christmas."

Then, too, after the slight turnaround, Thurow predicted another downturn because, as a result of the increase in spending, interest rates will be pushed up. If the Federal Reserve does not change its policy, Thurow said, then it will tighten monetary policy and "squeeze the economy back down into a recession."

Instead of setting monetary policy on the amount of money in circulation, the Fed should also keep in mind short-term interest rates, Thurow said.

However, he added, "I don't think there's anything you can do at the Federal Reserve Board that is going to give America a healthy economy. You can do things at the Federal Reserve Board that's going to make it worse--and that's what they are doing at the moment."