We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question raised by Marc Levine on homogeneous SL_n-spaces. At the end, we provide an application to the local-global principles for embeddings of étale algebras with involution into central simple algebras with involution.