Actomyosin bundles frequently form through aggregation of membrane-bound myosin clusters. One such example is the formation of the contractile ring in fission yeast from a broad band of cortical nodes. Nodes are macromolecular complexes containing several dozens of myosin-II molecules and a few formin dimers. The condensation of a broad band of nodes into the contractile ring has been previously described by a search, capture, pull and release (SCPR) model. In SCPR, a random search process mediated by actin filaments nucleated by formins leads to transient actomyosin connections among nodes that pull one another into a ring. The SCPR model reproduces the transport of nodes over long distances and predicts observed clump-formation instabilities in mutants. However, the model does not generate transient linear elements and meshwork structures as observed in some wild-type and mutant cells during ring assembly. As a minimal model of node alignment, we added short-range aligning forces to the SCPR model representing currently unresolved mechanisms that may involve structural components, cross-linking and bundling proteins. We studied the effect of the local node alignment mechanism on ring formation numerically. We varied the new parameters and found viable rings for a realistic range of values. Morphologically, transient structures that form during ring assembly resemble those observed in experiments with wild-type and cdc25-22 cells. Our work supports a hierarchical process of ring self-organization involving components drawn together from distant parts of the cell followed by progressive stabilization.