Unless administration officials and Congress move quickly to cut federal deficits, interest rates are likely to begin to climb again soon and economic recovery may be reversed, the chairman of the American Stock Exchange warned yesterday.

"What started out to be the beginning of a recovery could very well turn back into a recession that's even deeper than the one we've come out of," said Arthur Levitt Jr. Levitt is also chairman of the American Business Conference, a Washington lobbying group.

He said it is "unrealistic," however, to expect a balanced federal budget any time soon, suggesting that he sees no need to immediately set spending targets, only to move the budget projections for fiscal 1984 and 1985 in "the right direction."

"The question is more what is the approach of government going to be toward these deficits," Levitt said. "Are we going to have the kind of adversarial relationship with labor and business and government carping at one another creating the kind of runaway budget deficits which would suggest to our company CEO's chief executive officers that the budget is totally out of hand?"

Levitt, interviewed on "Face the Nation" (CBS, WDVM), also said that unless there are indications during this year's current congressional session of a bipartisan effort to cut deficits in 1984 and beyond, the stock market gains of the past six months are also likely to be reversed.

The defense budget has to be "examined very carefully and pared," Levitt said. "Anytime you see $1.6 trillion being spent over a three-year period, the business community and the country as a whole believes there are economies and efficiencies" that can be found.

But he said it would be a "serious mistake to consider any new taxes at this time" and opposed any effort to wipe out either this year's tax cuts or an administration plan to add new taxes if the deficits grow in the future.