Sales of new homes in the nation surged again last month to a seasonally adjusted rate of 648,000 houses, the highest number since August 1980, the federal government said yesterday. The report came, however, as concern mounted that rising mortgage interest rates may soon undercut the housing recovery.

Interest rates have continued to creep upward, and an industry analyst predicted the Department of Housing and Urban Development soon will order another half-a-point rise--to 12 1/2 percent--in the FHA- and VA-insured interest rate, the second within a month.

Discount points charged with FHA loans stood at seven yesterday, the number that triggered the June 7 increase in the FHA rate from 11 1/2 percent to 12 percent, according to Mark J. Riedy, executive vice president of the Mortgage Bankers Association.

A point equals one percent of the mortgage amount, and is charged either to buyers or sellers. To make loans saleable in the secondary mortgage market, lenders must produce a yield competitive with other types of investments. To produce that yield, lenders give investors a discount, and get their money back in the form of points charged.

Rates on conventional markets hovered around 13 1/2 percent this week, perilously close to the 14 percent that many in the housing industry feel is the threshold where home sales being to drop off sharply.

The May sales of new homes were 4 percent higher than sales in April, which were revised upward to a seasonally adjusted 621,000 after the initial report last month, and 68 percent more than sales in May 1982. Similar increases in sales of existing homes was reported recently by the National Association of Realtors, which said a seasonally adjusted total of 2.86 million units were sold in May, a 5 percent increase over April.

Industry leaders said the high level of home sales can be sustained for the next couple of months. The rising interest rates, however, "create a cloud on the horizon," according to Jack Carlson, chief economist of the Realtors' association.

The head of the National Association of Home Builders, Harry Pride, said the May sales showed that the housing recovery is stronger and more widespread than many economists had predicted, but that "to sustain this pace in the months ahead, the recent upward trend in interest rates must be reversed."

Prices of new homes were sharply up, according to the Commerce Department. The average price last month was a startling $90,700, or 4.9 percent higher than the year ago price of $86,500. The median price in May was $75,900, up 9 1/2 percent from May 1982, when the figure was $69,300.