The actin cytoskeleton shapes cells and also organizes internal membranous compartments. In particular, it interacts with membranes in intracellular transport of material in mammalian cells, yeast or plant cells. Tubular membrane intermediates, pulled along microtubule tracks, are involved during these processes, and destabilize into vesicles. While the role of actin in this destabilization process is still debated, literature also provide examples of membranous structures stabilization by actin. To directly address this apparent contradiction, we mimic the geometry of tubular intermediates with preformed membrane tubes. The growth of an actin sleeve at the tube surface is monitored spatio-temporally. Depending on network cohesiveness, actin is able to stabilize, or maintain membrane tubes under pulling. Indeed, on a single tube, thicker portions correlate with the presence of actin. Such structures relax over several minutes, and may provide enough time and curvature geometries for other proteins to act on tube stability.