President Reagan dealt cautiously with the touchy issues of deficits and taxes today, claiming that "strong economic growth will keep deficits coming down" and saying no new program is necessary to reduce them.

"The deficit we have to face is an effect, not a cause," Reagan told the Chicago Economic Club. "The cause is when government takes too big a percentage from the private sector, you're going to have economic troubles . . . . Government is going to become a drag on the economy. And this is what we're trying to cure."

Reagan reiterated that he would turn to tax increases in a second term only as "a last resort" if a combination of growth and spending cuts failed to lower the deficit to acceptable levels.

Administration officials estimate that the federal budget deficit this year will be $173 billion. It was $58 billion the last year of the Carter administration.

A Reagan aide said the speech avoided breaking new economic ground on the theory that "if it ain't broke, don't fix it." It also avoided opening new lines of political discourse with Reagan's challenger, Democratic nominee Walter F. Mondale, who trails the president in most polls.

In contrast to the rousing and emotional speeches that Reagan gave at campaign rallies and to the American Legion earlier in the week, today's speech was designed to be less partisan and "more presidential" in tone.

Reagan used this same forum four years ago to back away from his claim that he could balance the budget during his first term. But his advisers provided information at the time projecting a budget surplus of $28 billion in fiscal 1984.

Today, one of Reagan's few applause lines came when he reiterated his call for a constitutional amendment requiring a balanced budget and for presidential authority to veto line items in federal appropriations.

Answering a series of carefully screened questions submitted in writing, Reagan mainly stuck to familiar formulations but said incorrectly that there have been federal deficits "every year since World War II." According to the budget documents Reagan sent to Congress earlier this year, there have been eight budget surpluses during this period, five of them during Democratic administrations.

Reagan said in response to a question that he would "continue to do two things . . . in attacking the deficits." One is to promote policies that encourage economic growth and increase federal revenues. And the other is to continue efforts to reduce federal spending.

Reagan said that as government revenues increase and spending declines "there must be a point at which those two will meet." Only if that failed to happen, he said, should the "last resort" of tax increases be considered.

"If you come to a point where you've done all you can do with regard to economy recovery and the revenues fall short of that line and you've done all you can do to bring government down to be as efficient and economical as it should be and still perform the services that you expect of government and those two are apart, then you have to look at your tax system to bridge that difference," Reagan said.

On another economic issue, Reagan dodged a question about whether, as recommended by the International Trade Commission, he would approve import quotas on foreign steel when the matter comes before him later this month. But his answer emphasized basic opposition to protectionism.

Reagan also used his speech to denounce "ill-spirited divisiveness" and "bigotry," saying that "one of the good changes of recent years is that we have outgrown a lot of that nonsense."

"It is time we erased the last vestiges of intolerance, bigotry and unkindness from our hearts," Reagan said. "Decency demands this and so does history."