Reagan administration officials said yesterday that the economic recovery has become so broadly based and vigorous that it is now as strong as those that followed other postwar recessions.

The faster economic growth, however, will neither add to expected levels of inflation, nor will it cause an increase in interest rates, Treasury Secretary Donald T. Regan predicted at a National Press Club luncheon.

"We expect the prime rate to be down by the end of the year, lower than it is today," he declared.

Meanwhile, the Commerce Department said the index of leading economic indicators--which often foreshadows changes in the economy--increased 1.2 percent in May, the 11th gain in the last 12 months. Commerce Secretary Malcolm Baldrige called the increase "still another encouraging sign for the economy . . . that suggests that the recovery will remain vigorous in the months ahead."

President Reagan announced at his Tuesday night press conference that the administration was revising upward its forecast for economic growth for the four quarters of 1983 from 4.7 percent to 5.5 percent. The forecast for 1984 was raised to 4.5 percent from 4 percent.

Even with the speedier recovery, the civilian unemployment rate, which was 10.1 percent in May, is forecast to drop only to 9.6 percent in the fourth quarter of this year and to 8.6 percent late in 1984. Those estimates are 0.1 and 0.2 percentage points lower, respectively, than in the previous administration forecast.

The inflation prediction was virtually unchanged, with the GNP deflator estimated to rise 4.6 percent during 1983 and 5.0 percent in 1984. The 1983 figure was revised upward from 4.5 percent because of slightly higher than expected inflation so far this year.

Regan was ebullient as he spoke to the Press Club audience. He dismissed critics of the administration who focus only on the level of interest rates and the size of the federal budget defict "to the exclusion of other factors . . . They think of the recovery as a sprouting tree about to be chopped down; I characterize it as a sapling whose underground roots are far more extensive than the visible plant."

The Treasury secretary pointed particularly to financial markets where, he said, "In my 35 years of investment experience, I've never witnessed anything approaching the current explosion of confidence. Over the first five months of this year, corporations sold more than $21 billion of new equity common stock , or more than two-thirds the total issued in 1982 and close to the full-year totals in 1980 and 1981."

Martin S. Feldstein, chairman of the Council of Economic Advisers, told reporters that the recovery, which started slowly in the first quarter of this year, has now become a "median recovery" that in many ways is similar to the average of previous postwar recoveries.

Feldstein said, for instance, that the increase in industrial production in the five months from December to May was almost exactly in line with the earlier averages. The increase in total employment over the same five months, as shown by payroll records, is only slightly below that average.

The index of coincident economic indicators, one of which is industrial production, has risen 3.7 percent since December, an increase very close to that in earlier recoveries, the Commerce Department said.

The latest revision in the administration's forecast leaves it somewhat higher than that of most private analysts, Feldstein acknowledged. Nevertheless, he said, "I am more comfortable now about the forecast than I was in April" when the previous one was released.

Jerry Jasinowski, chief economist for the National Association of Manufacturers, said the new figures "are certainly at the upper end of the forecasts. Still, he added, "there's not a lot of room to disagree with the president" that recovery will be strong through the end of this year.

Feldstein agreed that there is some "downside risk" to the forecast from interest rates. He noted that rates "have moved up sharply" in recent weeks, adding to the strength of the dollar on foreign exchange markets and depressing exports. "You have to wonder whether at some point the high rates might tip too many sectors" of the economy back toward recession, he said.

The 1.2 percent increase in the leading indicators was the smallest monthly rise so far this year. The other increases ranged from 1.4 percent in April to 2.9 percent in January.

Seven of the 12 indicators rose in May, with the rate of net business formation adding the most to the index's increase. Three of the indicators fell, one was unchanged and one was not yet available, the department said.