In the last years, studies that question important conceptual and methodological aspects in the field of ecological niche modeling (and species distribution modeling) have cast doubts on the validity of the existing methodologies. Particularly, it has been broadly discussed whether it is possible to estimate the fundamental niche of a species using presence data. Although it has being identified that the main limitation is that presence data come from the realized niche, which is a subset of the fundamental niche, most of the existing methods lack the ability to overcome it, and then, they fit objects that are more similar to the realized niche. To overcome this limitation, we propose to use the region that is accessible to the species (based on its dispersal abilities) to determine a sampling distribution in environmental space that allow us to quantify the likelihood of observing a particular environmental combination in a sample of presence points. We incorporate this sampling distribution into a multivariate normal model (Mahalanobis model) by creating a weight function that modifies the probabilities of observing an environmental combination in a sample of presences as a way to account for the uneven availability of environmental conditions. We show that the parameters of the modified, weighted-normal model can be approximated by a maximum likelihood estimation approach, and used to draw ellipsoids (confidence regions) that represent the shape of the fundamental niche of the species. We illustrate the application of our model with two worked examples: (i) using presence points of an invasive species and an accessible area that includes only its native range, to evaluate whether the fitted model predicts confirmed establishments of the species outside its native range, and (ii) using presence data of closely related species with known accessible areas to exhibit how the different dispersal abilities of the species constraint a classic Mahalanobis model. Taking into account the distribution of environmental conditions that are accessible to the species indeed affected the estimation of the ellipsoids used to model their fundamental niches.