The government yesterday cut a half percentage point off the interest charge for single-family home mortgages backed by the Federal Housing Administration and the Veterans Administration, reversing a string of summer-long increases in the rate.

Spokesmen for the housing industry reacted favorably to the announcement of the rate cut, but expressed some worries that it may have come too soon and that the government might find itself having to boost the rate again before long.

Effective today, the rate on FHA and VA mortgages that have the same monthly payment for the life of the loan will be 13 percent, down from the 13.5 percent rate that had prevailed since July 29--when the rate was boosted a full point, from 12.5 percent.

For mortgages on which the monthly payment gradually rises, the government ceiling was lowered to 13.25 percent from 13.75 percent.

Secretary of Housing and Urban Development Samuel R. Pierce said the rate cut should make housing affordable for more Americans.

He said he moved to cut the rate because the factors that have served to boost long-term interest rates since May have eased considerably and that credit markets have been reassured "that economic recovery will not reignite inflation."

Pierce cited a slowdown in the rate of growth of money and a moderation in retail sales and orders for durable goods as factors that should calm long-term lenders.

Not all executives in the housing industry believed Pierce's rationale for lowering the ceiling rates. If the administration sets the rate too low for its mortgages, lenders make up the difference between the rate on conventional mortgages and government rates by charging money "up front." The rate on conventional mortgages today is between 13.75 percent and 14 percent.

The up-front charges are usually measured in terms of a percentage of the mortgage loan. One point, for example, is the equivalent of 1 percent of the loan. On a $60,000 loan with five points, charges for points would total $3,000.

Assistant HUD Secretary Philip Abrams said another reason the agency decided to lower the ceiling rate was that lenders are cutting the points they charge on government-backed loans. The latest weekly poll showed lenders charging 2.64 points for level payment mortgages, compared with 4.75 points the week before.

Mark Riedy, executive vice president of the Mortgage Bankers Association, said he was "pleased to see the decline," but said the "administration moved awfully quickly in lowering the rate." Riedy said he hoped the cut was not "premature."

Riedy said politics may have pushed the administration into lowering the rate.

Jack Carlson, executive vice president and chief economist of the National Association of Realtors, said the rate is "good news provided lenders don't again find it necessary to charge an excessive number of points."

Government rates peaked at 18.5 percent in November 1981, then declined steadily to 11.5 percent by last May. Since then, the rate has risen first to 12 percent, then to 12.5 percent and finally to 13.5 percent on July 29.

The home building industry was in a mini-boom early this year, as declining mortgage rates made housing affordable to many buyers who had been shut out of the market when rates were higher. Since rates began to climb again, however, more and more potential buyers were squeezed out.

New home sales declined 2.9 percent between May and June. Housing starts for single-family homes fell 3.1 percent in June and 11.9 percent in July.