Groups representing several Cadillac dealers are urging General Motors Co. to rethink a new retail strategy for the luxury brand, saying the plan is an attempt to steer around dealer franchise laws that have long prevented auto makers from closing dealerships.

In a letter signed by dealer associations from seven states, Cadillac President Johan de Nysschen was accused of creating a program that they consider “is the most serious attack on their survival they have seen." Mr. de Nysschen has been in the process of rolling...