Sharply rising energy costs helped send producer prices soaring by 1 percent last month, the biggest monthly increase in more than a year, the government reported yesterday.

The overall producer price increase in June was equivalent to an annual increase of 13.3 percent, the Bureau of Labor Statistics reported. The largest rise since March, 1981, this ended a string of unusually small increases in producer prices. In the four preceding months they had been stable or had declined.

Economists in an out of the Reagan administration appeared to agree yesterday that the June increase will probably prove to be just a temporary blip because oil prices, after rising rapidly in May and June, have stabilized.

A 4.1 percent jump in energy prices accounted for about half of the June increase in producer prices, the government reported. And with the ending of various rebate schemes last month, prices of new cars also rose 1.9 percent. Prices of light trucks rose by 3 percent.

Excluding energy and new cars, prices charged by producers for finished goods rose at an annual rate of 3 1/2 to 4 percent in May and June, a Commerce Department official said yesterday. Producer price inflation for the first six months of the year, even including the June number, was 2 1/2 percent at an annual rate. However, this was heavily influenced by falling energy prices in the early months of the year.

Robert Dederick, Commerce undersecretary-designate for economic affairs, said yesterday that the underlying level of inflation across the economy is still between 5 and 6 percent.

The recession has had a major downward impact on prices, and separate official reports this week indicated that the economy remained very weak in June.

The Federal Reserve Board reported yesterday that the nation's factories operated at 69.8 percent of their capacity last month, the second lowest rate on record. It was a drop of 0.6 percentage points from May. This measure has dropped below 70 percent only once before, in the spring of 1975. A year ago it stood at 79.6 percent.

Commerce Department economist Robert Ortner said yesterday that the drop in factory use would help curb inflation.

"With the industrial operating rate now below 70 percent there is very little inflationary pressure in the economy," he said. "There is a lot of slack which should be taken as a sign inflation should remain moderate over the next year or two."

Some analysts say persistent high interest rates have kept the economy in recession. This month, money market rates have begun to ease substantially as the Federal Reserve has injected more reserves into the banking system and has reported lower-than-expected figures for the money supply.

Yesterday the Federal Reserve announced a $5.9 billion increase in the narrow M-1 measure of money--currency in circulation and checking accounts--for the week ended July 7. This was toward the bottom end of the range of expectations, and should allow for further interest rate declines next week.

The markets had feared a surge in the money supply during the first week in July because of increased Social Security benefits and the tax cuts that went into effect July 1.

The White House emphasized to reporters that, while yesterday's price report showed a jump in inflation in June, price gains over the past year have been moderate. In the 12 months ended in June, producer prices increased 3.5 percent, compared with an increase of more than 11 percent in the 12 months before President Reagan took office, White House spokesman Larry Speakes said.

The consumer price index, which measures a slightly broader range of goods including services, rose by 1 percent in May. The June report is due next week.

The producer price index for finished goods was unchanged in May after rising 0.1 percent in April and falling in February and March.

Crude material goods prices dropped 0.1 percent in June, yesterday's report showed. This followed increases of 1.8 percent and 2.2 percent in April and May.

Prices of goods at the intermediate stage of production were up 0.3 percent last month, BLS said, following a rise of 0.1 percent in May and declines in the three previous months.

Food prices rose 0.5 percent in June, the report said, following a rise of 0.7 percent in May.

Capital equipment prices rose 0.8 percent last month, after climbing 0.4 percent in each of the previous three months.