The problem is to solve a linear least squares system \(Ax=b\) with real \(A\in\mathbb{R}^{m\times n}\). First the construction and properties of different variants (i.e., the direct and the extended direct version) of the Kaczmarz's projection iteration are recalled from \textit{C. Popa} [An. Univ. Timis., Ser. Mat.-Inform. 40, No. 2, 107--125 (2002; Zbl 1073.65522)]. In these methods additional directions are introduced for the projections in the iteration steps. Next all this is generalized to the block case. That means that the matrix is subdivided in blocks (that may have different sizes) and that instead of projections onto (orthogonal complements of) one-dimensional spaces, these become subspaces of higher dimension. The properties of the one-dimensional versions are generalized and proved for these block versions. Three medium size numerical examples are given from which conclusions are drawn like (1) being direct methods they have a bad fill-in property, although the fill-in elements are very small; (2) computational cost depends strongly on how the least squares problems (Moore-Penrose inverses) are computed in the projection steps; and (3) round-off analysis is needed to analyse the stability of the method.