Enveloped viruses include the most dangerous human and animal pathogens, in particular coronavirus, influenza virus, and human immunodeficiency virus (HIV). For these viruses, receptor binding and entry are accomplished by a single viral envelope protein (termed the fusion protein), the structural changes of which trigger the remodeling and merger of the viral and target cellular membranes. The number of fusion proteins required for fusion activity is still under debate, and several studies report this value to range from 1 to 9 for type I fusion proteins. Here, we consider the earliest stage of viral fusion based on the continuum theory of membrane elasticity. We demonstrate that membrane deformations induced by the oblique insertion of amphipathic fusion peptides mediate the lateral interaction of these peptides and drive them to form into a symmetric fusion rosette. The pulling force produced by the structural rearrangements of the fusion protein ectodomains gives additional torque, which deforms the membrane and additionally stabilizes the symmetric fusion rosette, thus allowing a reduction in the number of fusion peptides needed for fusion. These findings can resolve the large range of published cooperativity indices for HIV, influenza, and other type I fusion proteins.