Abstract class contains a constructor because there is a chance of existence of an instance variable but inside the interface, there is no chance of existence of the instance variable. Basically constructor is used to initializing the instance variable. There is no existence of instance variable inside interface because of that no need of constructor inside the interface.
An interface does not have an instanced implementation, hence no constructor. The job of the constructor is to initialize the member variables. Abstract class can have member variables. Interface doesn't.