In this paper, we propose a new strategy of estimation for the survival function S, associated to a survival time subject to interval censoring case 2. Our method is based on a least squares contrast of regression type with parameters corresponding to the coefficients of the development of S on an orthonormal basis. We obtain a collection of projection estimators where the dimension of the projection space has to be adequately chosen via a model selection procedure. For compactly supported bases, we obtain adaptive results leading to general non-parametric rates. However, our results can be used for non compactly supported bases, a true novelty in regression setting, and we use specifically the Laguerre basis which is R +-supported and thus well suited when nonnegative random variables are involved in the model. Simulation results comparing our proposal with previous strategies show that it works well in a very general context. A real data set is considered to illustrate the methodology. MSC 2010 subject classification: 62N02–62G05