Federal budget deficits will continue to grow, even after the long-promised economic recovery is complete, and will top $200 billion a year in the late 1980s unless there are further spending cuts or tax increases, according to estimates from the Office of Management and Budget.

Administration sources yesterday confirmed the estimates, which, they said, assume the economy will grow at more than a 3.5 percent rate during 1983, adjusted for inflation, and at a 4 percent rate for the next five years.

The estimates directly conflict with President Reagan's assertion Monday in a speech to the National League of Cities that the only way to eliminate "the monstrous proportions of our deficit . . . lies in stimulating the economy and increasing productivity." However, the new figures also help explain Reagan's unexpected emphasis on the size of the deficits and the apparent attempt to lay the political groundwork for publicly acknowledging them.

Reagan, to the consternation of some administration officials, also said, in a passage a White House aide said he wrote himself, " . . . 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."

Since a full economic recovery will not close the ever-widening gap between revenues and outlays, the only way the deficit could possibly be reduced would be by trimming spending or raising taxes, the officials said.

Reagan's chief economic adviser, Martin Feldstein, has made a series of speeches in the last three weeks in which he has blamed rising deficits for a range of economic ills and declared that if they are not reduced the tide of red ink will abort the recovery.

Some administration officials are hoping the president will be willing to consider a substantial package of spending cuts and revenue raising measures, including some new energy taxes, to reduce the prospective deficits. But after the president's Monday speech they are more doubtful than ever that he will move very far in that direction.

On the spending side, the new OMB estimates assume continuation of present domestic programs and Reagan's original high track for defense outlays for 1984 and beyond. Congress lowered the defense spending figures when it passed its 1983 budget resolution earlier this year. Shortly after its adoption, however, the president said he did not feel bound by the lower defense numbers except for 1983 even though they were part of an overall budget compromise to which he had agreed.

Similarly, on the revenue side, the estimates assume no changes in taxes except those called for by present law, such as next year's 10 percent cut in most current personal income tax rates.

In the last official budget estimates, released July 30, OMB put the 1983 deficit at $115 billion, up only slightly from the 1982 figure, which later turned out to be $110.7 billion, by far the largest deficit in U.S. history.

With the delay in the long-awaited economic recovery, the fiscal 1983 deficit estimate has now risen to about $170 billion. Deficits in off-budget agencies that are financed by direct federal borrowing come to an additional $18 billion.

The deficit for fiscal 1984 is expected to be several billion dollars larger, primarily as a result of additional personal and business tax cuts in 1983 and 1984 and steadily rising military outlays. Together those elements offset the revenue gains and somewhat lower spending, such as for unemployment benefits, flowing from the assumed economic recovery.

By 1985 the deficit jumps to about $195 billion, the administration sources said. After 1985 the deficit figures begin to level off, after topping $200 billion. "They just don't come down," one official said.

Congressional Budget Office officials, who had not been briefed by OMB on any of the new estimates, said the large projected deficits "clearly are possible," especially with the higher defense spending figures.