The Reagan administration will publish a revised forecast later this month showing a resumption of economic growth at a higher pace than now expected by most private forecasters, administration officials said yesterday.

The new forecast, due about July 21, calls for the economy to expand at a 4 to 5 percent rate in the second half of this year and throughout 1983, with inflation running "within striking distance" of 6 percent, officials said. Many private forecasters, whose expectations for growth were already somewhat lower than those of the administration, recently have been revising their figures downward because of the persistence of high interest rates.

For instance, Data Resources Inc., a prominent economic consulting firm, two weeks ago dropped its forecast for the second half of the year by about a percentage point, seeing the gross national product rising at an annual rate of only 2.7 percent after adjustment for inflation.

Even if short-term interest rates should continue to fall, as they began to do this week, few economists expect them to fall far enough to cease to be a drag on the economy.

Long-term interest rates, which are critical to investment and housing, are expected to fall very little this fall even if short-term rates drop.

A group of economists that met yesterday with Congressional Budget Office officials to provide advice on the outlook also suggested that growth will be lower, and perhaps much lower, than called for in the last CBO forecast, which roughly paralleled that of the administration in terms of the second half of 1982 and 1983, according to one participant. The group meets regularly with CBO officials. In effect, the forthcoming administration forecast is similar to the one made last winter and published with the fiscal 1983 budget except that the recovery has been delayed by several months. At that time, administration economists, and many private forecasters, too, thought the turnaround from recession would come during this spring and that by this month the recovery would be well under way.

Instead, Murray L. Weidenbaum, chairman of the president's Council of Economic Advisers, has acknowledged that the "signs" of a recovery--new orders and higher production and employment--are not visible even now.

"We continue to expect a second-half recovery that will be sustained in 1983," one official said yesterday. "The first four to six quarters may not approximate past recoveries but growth will still be in the 4 percent to 5 percent range."

In recoveries not plagued by high interest rates, gross national product has risen at rates of 6 to 8 percent during the early stages of the expansion.

Economists both in and out of government are counting on an increase in consumer spending to spark the recovery, partly as a result of this month's tax cut. But business investment is falling, and unless interest rates come down substantially, there is a serious question whether investment in either housing or business plants and equipment will increase.

If they do not, Weidenbaum has said, the "second stage" of the recovery may not occur. Without such a second stage, the growth seen in the upcoming forecast for 1983 is unlikely to be achieved, in the opinion of most analysts.

Each month of delay in the beginning of the recovery also increases the danger of serious problems in financial markets and of increases in corporate bankruptcies. "The difficult financial condition of many companies is a barrier to recovery," one of the administration officials acknowledged. "The bankruptcy figures are really worrisome."

Dun & Bradstreet Inc. reported this week that business failures in the first six months of 1982 exceeded the total for all of 1980 and were up nearly 50 percent from 1981. Altogether, 11,948 businesses went bankrupt in the first half of the year, with 522 failing in the week ended July 1.

The failure of a major bank in Oklahoma last week also has added to concerns about financial markets, with a number of analysts suggesting that less creditworthy companies will soon find it harder to get credit and that it will cost them even more than it has been to date, compared to interest rates being paid by more creditworthy firms.

Meanwhile, continued softness in the economy could swell the federal budget deficit.