Consumer prices rose only 3.9 percent during 1982, the smallest increase in inflation since 1972, when price controls were in effect, and significantly less than the 8.9 percent increase in 1981, the Labor Department reported yesterday.

In December alone, the Consumer Price Index dropped 0.3 percent as gasoline prices and mortgage interest rates fell and the cost of most other goods and services rose modestly. That decline, and a similar one last March, were the only two that have occurred in the index since 1965.

A separate report from the Commerce Department gave one of the strongest indications yet that an economic recovery is on the way. New orders received by manufacturers for durable goods, such as cars, machine tools and military equipment, rose a record 12 percent in December.

The surge in orders, with about three-fourths of the gain coming in the defense area, should mean increased production and rising employment levels soon. The industries producing durable goods have been among those hardest hit by the recession.

At the White House, Martin Feldstein, chairman of the Council of Economic Advisers, called the progress against inflation "truly remarkable" and said, "There is good reason to believe that we have finally ended the upward spiral of inflation that began in the mid-1960s."

Feldstein said an economic recovery "is likely to begin" this quarter and that during 1983 "we'll see the unemployment rate come down without any significant increase in inflation."

Feldstein gave much of the credit for lower inflation to the Federal Reserve's monetary policy, which he said has been "the principal policy that has helped bring down inflation. The administration has been basically supportive of the Fed policy . . . and I think the Fed would acknowledge that without the administration's support, it would have had a much more difficult time in achieving this decline . . . . "

The CEA chairman acknowledged that tight money and high interest rates also have been responsible for slowing economic activity and raising unemployment, which was 10.8 percent in December.

But Feldstein also said that, "Starting this year, we are going to see inflation and unemployment continuing to move in the right direction. We'll see the unemployment rate come down without any significant increase in inflation."

The unemployment rate should start to fall "a couple of months" after an economic recovery begins, probably this quarter, though "there is a great deal of uncertainty about the timing of the beginning of a recovery . . . ," Feldstein said.

Mortgage interest rates, which account for nearly 11 percent of the entire CPI, fell 12.5 percent during 1982, the largest decline since records were first kept in 1952. That drop, along with a marked slowdown in energy price increases, was primarily responsible for the decline in inflation over the last year.

Economists have believed for years that housing prices and mortgage interest rates have had too prominent a role in the CPI, and beginning with the CPI for January these components will be replaced with a new component that will measure changes in rental prices.

The Bureau of Labor Statistics has been publishing an experimental measurement similar to the one it will begin to use officially this month. According to that measurement, the CPI rose 5 percent from December, 1981, to December, 1982, rather than the 3.9 percent figure; and for the month of last December, consumer prices rose 0.3 percent instead of falling 0.3 percent.

The BLS also reported that grocery store prices dipped 0.5 percent last month and were up only 2.2 percent during the year.

Gasoline prices went down 1.8 percent in December and 6.6 percent for the year, the largest decline since 1935, the first year such records were kept. Fuel oil, coal and bottled gas prices rose only 0.9 percent for the year and fell 0.4 percent in December. Natural gas and electricity prices, on the other hand, shot up 14.1 percent last year.

Medical care costs climbed 0.7 percent last month and 11 percent for the year.

Transportation costs went up only 1.7 percent for the year, as the decline in gasoline costs offset a 10.9-percent jump in used-car prices. New-car prices, which rose 0.6 percent in December, increased only 1.6 percent during the year.

Meanwhile, Commerce said orders for durable goods rose $8.5 billion, or 12 percent, last month to a level of $79.1 billion. Orders for defense goods, including ships and aircraft parts, rose $6.9 billion, up a huge 135 percent from November.

Outside the defense area, orders rose a more-modest $1.6 billion, or 2.4 percent. However, analysts noted the gains were spread across a wide range of industries, probably indicating a recovery is imminent.