An early introduction of new, high-mileage American-built cars pushed U.S. auto sales off to a fast start in October, as the five major domestic companies reported sales 12 percent above those in the first 10 days of October a year ago.

The comparison was distorted by the differing introduction dates in the two years. Last year, almost all new-model introductions were in the second 10-day reporting period of October. This year, Ford Motor Co. and Chrysler Corp. held early-October introductions, and General Motors Corp. and American Motors Corp. had late-September unveilings.

Sales were 223,402 cars for the five companies against 200,141 in the 1979 period.

The annual selling rate was the same as September's -- 6.6 million cars for the domestic companies.

Chrysler Corp. showed a 21 percent increase from 23,017 cars to 27,860, the largest gain of any company. Chrysler said Monday the 10,217 K-car compacts it sold in the period was the best first-period showing of any model in the company's history.

General Motors Corp. enjoyed a 15 percent increase from 111,399 cars to 127,573. Ford Motor Co. had an increase of 8.6 percent from 56,172 to 61,029, including 11,020 of its new front-wheel-drive subcompact Escort and Lynx models.

American Motors Corp. sold an estimated 4,200 cars.The estimate is necessary because AMC gives out figures only at the end of the month.

Volkswagen of American Inc., whose 1981 introductions come later this month, had a 40 percent decline from 4,553 to 2,740.

Industry executives pronounced themselves happy with their first increase from a year-ago sales period since Jan. 21 to 31, when sales were up 1.2 percent.

"The proof of the strength of these new models is that our dealers delivered close to half of their available cars [on the first day], all equipped with manual transmission," said Bennett E. Bidwell, vice president in charge of Ford's car and truck group.

First-day sales rarely reached 40 percent of available cars.

The good showing left the U.S. industry still 22 percent behind the 1979 sales pace to this point in the year -- 5.14 million cars to 6.55 million. 1

For the year to date, Ford was down 32 percent, 1.68 million to 1.14 million; GM was off 17 percent, 3.87 million to 3.22 million; Chrysler was off 34 percent, 758,306 to 530,167; AMC was up 5.5 percent, 117,662 to an estimated 124,607; and VW was up 17 percent, 124,929 to 146,466.

J. Paul Bergmoser, Chrysler's president, predicted yesterday that the company will show reduced losses for the third quarter, the first time in 30 years the company had improved results from the second quarter of the year to the third.

The third quarter is almost always the slowest of the year for auto companies because of the summer sales lull and the expense of launching new models. In the second quarter, Chrysler lost $536 million.

The company has said it expects a profit in the fourth quarter and for the entire year of 1981 -- a viewpoint disputed by many Wall Street analysts. t

In another development, the United Auto Workers yesterday receivd a $1.3 million grant from the Carter administration to establish "crisis centers" for jobless workers in eight cities with high auto unemployment.

Labor Secretary Ray Marshall said the program, one phase of Carter's plan for aiding the auto industry, is designed to assist auto workers who have exhausted unemployment insurance and other benefits.

Marshall's spokesman, Frank Greer, said the aid program has been under development for months and "is not politically motivated."

The crisis centers are planned tentatively to be set up at UAW offices in Detroit, Flint, Pontiac and Saginaw, Mich.; Anderson, Indianapolis and Kokomo, Ind.; and Cleveland.

The workers will receive help in getting more benefits to which they may be entitled, including welfare, food stamps, veterans benefits, legal aid and employment assistance, Marshall said.

The centers also will provide counseling on credit and mortgage protection, marital and financial problems, emotional stress, alcohol and drug abuse and educational guidance.

The grant comes on top of a $1.6 million national on-the-job training contract previously awarded to the union.

Some 250,000 auto workers are on indefinite layoff because of the industry's slump.