For the first time, American Honda Motor Co. is offering cash incentives to its dealers through the end of May to help spur lagging car sales.

Honda, whose dealers were once able to charge the full sticker price of a car or even an added premium in some instances, declined to call its program an incentive, terming it instead an "advertising support plan.""It may be a matter of semantics, but this is certainly not a retail incentive in the sense that most buyers think of," company spokesman Jeff Leestma said. "It is not a cash-back or a rebate or a low-rate financing plan. What it is is an advertising support plan."

Each of Honda's 934 U.S. dealers has been assigned a specific sales target through May 31, he said. Any dealers who reach that goal will be paid an extra $100 per car by American Honda.

If the dealer exceeds that goal by 15 percent, an additional $100 per car is given. Dealers who attain more than half their assigned goal by April 30 will earn an extra $100 for each vehicle sold that month, bringing the maximum support to $300 per car.

Honda expects dealers will use the extra money to bolster advertising programs. The incentives do not cover Honda's Acura line.

Honda's U.S. sales during the first three months of 1989 were 132,729 cars, down 9.1 percent from 146,006 cars sold in the year-ago period.

Its supply of imported cars, however, swelled to 40 days, compared with 36 days last month and 10 days a year ago. Dealer inventories of its domestically built cars, which account for about 40 percent of its U.S. sales, were equivalent to 29 days, compared with 30 last month but 11 days a year ago.

Leestma attributed Honda's sales decline and rising inventories to the fact that the entire industry has become extremely competitive, with new aggressive sales promotions from General Motors Corp., Ford Motor Co. and Chrysler Corp., as well as several import carmakers.

He also said the new car market in general has been growing weaker because of rising interest rates and buyer concern over inflation.