Led by General Motors Corp., the nation's automakers today reported continued improvement in car sales, with a 12.2 percent increase for the middle of May compared with the same 10-day period a year ago.

Some market analysts saw signs of the beginnings of a recovery from the industry's devastating three-year sales depression, but industry officials cautioned that it is too soon to tell. Ford Motor Co. Chairman Philip Caldwell said it will take until June to determine whether a recovery is under way.

"Yes, we're on the way back, but we're still far below normal," said Detroit auto industry analyst Arvid Jouppi.

GM, which led the domestic industry with a 23 percent increase in sales in the mid-May sales period compared with 1981, still is offering car buyers a 12.8 percent financing rate, which is equal to an average savings on financing charges of $825 a car.

That incentive is due to end next Monday, and GM is hoping to avoid a fall-off in sales when that happens. GM sold 103,977 cars in the first 10 days of this month and 144,032 cars in the mid-May period. Sales for the Chevrolet division, which has done particularly poorly because of consumer reaction to higher prices and financing costs, rose 33 percent over the mid-May period a year ago.

The mid-May increase for the domestic industry followed an 18.2 percent boost in the first 10 days of May. The last back-to-back sales increases were in from Aug. 1 to Sept. 20 in 1981. At that time, as now, General Motors Corp. offered low interest rates on car loans financed through its subsidiary, General Motors Acceptance Corp.

Ford Motor Co. said its sales were off 0.6 percent in mid-May. Chrysler Corp. car sales rose 5.5 percent.

The 10-day estimate for American Motors Corp. was down 32.6 percent from a year earlier, and Volkswagen of America Inc. was off an estimated 62.9 percent.

GM's sales of 144,032 cars in the mid-May period is up from 117,074 in the 1981 period. Ford said it delivered 44,748 cars in the 10 days this year, down from 45,001. Chrysler sold 21,341 cars, up from 20,226.

AMC's estimate of 3,400 was down from 5,043 in the period last year, and VW's 1,660 estimate was off from 4,477 a year ago.

The car makers said they sold 215,181 autos in compared with 191,821 in the year-ago period. The mid-May sales rate is equivalent to a seasonally adjusted annual rate of about 6.7 million cars.

For the month so far, the carmakers have delivered 374,393 cars, up 14.7 percent from 326,473 sold in the first 20 days of May last year.

The total year-to-date industry count was 2.27 million cars, down 12.3 percent from 2.59 million sold by May 20 last year.

GM stood at 1.4 million cars, down 10 1/2 percent from 1.57 million sold in 1981 by May 20. Ford said it has delivered 528,559 cars, down 8.8 percent from 579,792 by this time last year. Chrysler sold 269,926 cars, down 15 1/2 percent from 319,360.