New automobile sales showed renewed vigor in the first 10 days of 1980, with overall volume down much less from the previous year than had been experienced during the final months of last year, major manufacturers reported yesterday.

Separately, Secretary of Transportation Neil Goldschmidt revealed that he was asked by President Carter this week to launch an extensive government examination of the auto industry and "the broad industrial network which touches and is touched by that industry."

The new study is to be completed in nine months, Goldschmidt said in a speech to the Economic Club of Detroit.

Although reporters said that Goldschmidt received a gernerally warm welcome from Detroit's auto industry and business establishment at yesterday's luncheon, industry veteran Henry Ford II had little enthusiasm for another federal study.

"You can study something to death, but I think they're going to have to make up their own minds pretty soon about how they're going to react to the situation in this country," said the Ford Motor Co. chairman, according to United Press International.

Sales of U.S. manufactured cars declined by just 4.4 percent in the first selling period of the new year with industry giant General Motors Corp. down only one percent, the auto companies reported. Late last year, sales had been down by about 20 percent from year-earlier levels.

Robert Burger, a vice president in charge of GM's marketing staff, described the initial sales report of 1980 as "a strong note" and he forecast continued sales strength as the year progresses. "The results of the past month, especially the sales records established by the Oldsmobile and Buick divisions in the Jan. 1-10 period, indicate that some of the people who have been sitting on the sidelines are now returning to the marketplace," Burger commented.

GM sold 98,883 cars in the recent 10 days compared with 99,872 a year earlier. Truck sales remained weak, however, with volume down 21 percent to 24,104.

Ford and the troubled Chrysler Corp. didn't participate in the overall sales rebound, with sales off by 17 percent and 18 percent, respectively.

But American Motors Corp. sales soared an estimated 88 percent and Volkswagen of America said Pennsylvania-built Rabbit sales jumped 64 percent.

Overall industry sales were 160,000 in early January compared with 107,415 a year ago. Ford sales totaled 37,271, down from 44,775; Chrysler was down from 18,945 to 15,458: AMC was up to an estimated 4,000 from 2,125 and VW was up to 4,388 from 2,680.

Analysts said the early January results were too little to amount to a trend and they noted that some dealer incentive programs have been in effect, as the manufacturers have tried to reduce an inventory backlog of 1.66 million cars on Dec. 31 -- enough for more than 70 selling days and the highest level since 1975.

With the auto industry operating at recessionary levels and more than 200,000 auto workers out of work this week, Goldschmnidt's speech yesterday was seen as an effort by the Carter administration to indicate that it is paying attention to Detroit's woes.

Goldschmidt told his audience that the government seeks "a working alliance of mutual respect" with the manufacturers, based on two premises:

Recognition by government that profit is the "driving force" that creates more jobs and a strong industrial base.

Acceptance by industry of government's role in representing "national and enviromental social goals, from which there can be no retreat."