President Reagan said today that only economic recovery, rather than budget cuts or tax increases, can reduce federal budget deficits that have grown to "monstrous proportions."

The president, who came into office promising to balance the budget by 1984, appeared to be preparing the country for huge federal budget deficits into the foreseeable future. He contended that they can be eliminated only by continuing to stimulate the economy with income tax cuts, which he says eventually will produce increased revenues.

"We have, as I've said, sizably reduced the annual increase in spending but there is no way we can eliminate, by budget cuts alone, the structural deficit built into the budget, nor can it be eliminated by raising taxes," the president said in a speech to the annual convention of the National League of Cities here.

He did not define what he meant by "structural deficit."

But a White House official said his remarks reflected a growing consensus in the administration that Reagan may have to live with very large deficits if the economy, as expected, recovers slowly and the president sticks by his tax cut and Pentagon budget expansion.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said on Sunday that Congress probably will not make big cuts in domestic or defense spending next year. He said the nation faces annual budget deficits of as much as $200 billion if the Federal Reserve Board does not help revive the economy by forcing interest rates down.

Associated Press last night quoted government sources as saying that budget director David A. Stockman's latest estimate for the current fiscal year shows a deficit of between $180 billion and $190 billion.

The sources also said Stockman sees even higher deficits in the following years, with that for 1987 in the range of $250 billion.

Reagan's emphasis today on economic growth as a means of reining in deficits marked a subtle but important shift from his earlier contention that deficits were largely the result of unnecessary federal spending that could be trimmed.

"The answer lies in stimulating the economy and increasing productivity," Reagan said of the deficit problem. "Even the trillion-dollar debt will become more manageable if it becomes a smaller percentage of the gross national product, which is the true measure of our wealth."

Speaking to about 4,500 city officials before departing for Washington this afternoon, Reagan delivered a vigorous defense of his three-year, 25 percent across-the-board tax cut program, but stopped short of publicly asking Congress to speed up the third phase due next July.

The president is expected to tell Republican congressional leaders Tuesday whether he has decided to ask Congress for a six-month acceleration in the final 10 percent installment of the tax cut. White House officials say that Reagan likes the idea but is concerned that such a request would overburden the lame-duck congressional session that began today.

In his comments here, Reagan said the tax cut "is already providing . . . the stimulus needed to get our economy moving again. This next installment, the so-called third year, will benefit working men and women more than anyone else and will have the most dramatic impact on our economy.

"Now this tax talk is no pipe dream," Reagan said. "Think back, when was the last time this country enjoyed real growth? When was the last period of boom, when unemployment dropped low, personal savings piled high, real wages grew, investment steadily increased, our industries were pumping at nearly full speed, and our gross national product was climbing?

"The last great period of American economic growth and low inflation rates was in the 1960s, following enactment of the tax rate cut proposed by President John F. Kennedy," Reagan said.

"President Kennedy knew as we know today: All the government boondoggles in the world won't fix what's ailing us. The only way to cure our problems is to get the economy moving again. And one of the best ways to stimulate the economy is to give the American worker a break and cut his or her tax rates," Reagan added.

He didn't mention in his speech today the $99 billion tax increase that he endorsed and Congress passed last summer. Describing his program as an "agenda for growth," the president also did not address the reasons why the first two installments of his tax cut did not meet his earlier promises that they would revive the economy.

But he made clear that he is now looking to economic growth to bring massive deficits down to size. Some Republicans, including Senate Budget Committee Chairman Pete Domenici (N.M.), have also argued recently that the deficit is widening so quickly it cannot be brought under control by budget cuts alone.

Treasury Secretary Donald T. Regan recently argued in a Cabinet session on the budget that the looming deficits may shrink if the economy improves. Regan has made a distinction between deficits that are "cyclical," or caused by the business cycle, and those that are "structural," caused by past and current fiscal policy.

An administration official said it is likely that the budget Reagan sends to Congress in January will envision large but declining deficits over the next few years.