The government's index of leading economic indicators improved moderately in November, while sales of new single-family homes jumped 12 percent to a two-year high, stirring hopes within the Reagan administration that an economic recovery of at least modest proportions will develop in the New Year.

A separate report showed that new claims for unemployment benefits were up slightly, although below recent peaks. Officials said that the increase was statistically insignificant. Nonetheless, new benefit claims continued at an uncomfortably high level, indicating there will be little reduction in the December unemployment rate when published Jan. 7.

The nationwide unemployment rate in November stood at 10.8 percent of the labor force, highest since 1940.

Commerce Secretary Malcolm Baldrige, commenting on a rise of 0.8 percent in the leading indicators' index--the seventh in the last eight months--said it was a favorable sign, both in "size and breadth," suggestive of an "economy moving toward recovery."

But Baldrige was quick to say that "the business upturn will be moderate in the early stages." He noted that the leading indicators index had gone up only 5.3 percent since March, well below the average post-war gain of 10.7 percent "in comparable periods."

In recent days, administration policy-makers have been trimming back their expectations for growth in next year's gross national product, following an unexpectedly weak final quarter of 1982. The "flash" report for the current quarter shows a minus 2.2 percent, instead of a predicted upturn.

Martin S. Feldstein, chairman of the Council of Economic Advisers, said in a telephone interview that "the plus" in the leading indicators is that the gain in November had spread beyond the financial components to the work week, retail sales and other indicators of real economic activity.

"The leading indicators are telling us that there's hope for a recovery, but they're not a prime indicator of when it will begin," Feldstein said. He continues to believe that recovery will be "of a modest nature." He added that "I haven't given up hope" that recovery might now begin in the first quarter of 1983.

New home sales in November rose to a seasonally adjusted annual rate of 569,000 from 509,000 in October, for the fourth monthly improvement in a row. November sales were 47 percent higher than the severely depressed level of a year before. The median price of a new house climbed to a record $74,200, from $69,300 in October.

Mark J. Riedy, executive vice president of the Mortgage Bankers Association of America, said that November home sales represent "the beginning of a fairly strong housing recovery," but its duration depends entirely on mortgage interest rates staying in the present 12-to-13 percent range.

Revisions in the leading indicators index for the preceding three months--all downward--indicate why many economists are skeptical of its forecasting potential. Earlier, the Commerce Department had reported a 0.2 percent decline for August; yesterday that was revised to 0.5 percent. A widely publicized 1.1 percent gain for September was moved down yesterday to 0.8 percent. And October's reported 0.6 percent gain was watered down to 0.3 percent.

In a statement released by his office, Baldrige said that the roadblock to recovery that had been caused by high interest rates is in the process of being dismantled. "The high level of interest rates that persisted into July caused the unusually long lag between the first rises in the leading indicators and the recovery. That logjam has now been broken. Housing starts have moved up decisively and other credit sensitive sectors should follow," the Commerce secretary said.

In November, seven of the 10 leading indicators rose. The gainers included the nation's money supply, the average work week, orders for consumer goods, building permits for future housing construction, prices of certain raw materials and stock prices. In the plus column also was a decline in initial unemployment claims during November.

Indicators showing weaker performance in November included business deliveries, total liquid assets and contracts and orders for new plant and equipment.

The Labor Department's new report on initial claims for unemployment benefits showed a rise to 544,000 on a seasonally adjusted basis in the week ending Dec. 18, from 533,000 the previous week. The new claims were below the weekly totals that exceeded 600,000 during most of the fall. But the new figure was the first increase in five weeks.