We created two-dimensional (2D) assemblies of tobacco mosaic viruses (TMVs) and characterized their structures using Atomic Force Microscopy (AFM) and X-ray scattering. The TMVs were adsorbed on an oppositely charged, fluid lipid monolayer supported by a solid substrate and submerged in a buffer solution. The lipid monolayer confined the viral particles within a plane, while providing them with lateral mobility so that overall the TMV assembly behaved like a 2D liquid. We controlled the inter-particle interaction by adjusting the chemical condition in the buffer to induce ordered TMV assemblies. We found that the presence of the lipid layer was essential for forming ordered TMV assemblies. Packed TMV assemblies formed on the lipid layer, with an average inter-particle spacing of 42 nm. By introducing Ca²⁺ ions into the buffer solution, we were able to improve the in-plane order within the TMV assemblies and reduce the average inter-particle spacing to 20 nm, compared to the TMV diameter of 18 nm. Quantitative analysis of the X-ray scattering data shows that the structural order within the TMV assemblies prepared under a Ca²⁺-free buffer solution is consistent with purely repulsive, electrostatic inter-particle interaction. In contrast, the structural order within Ca²⁺-induced TMV assemblies is consistent with the behavior of a fluid of sticky rods, implying the presence of a strong attraction between TMVs. In addition to the screening of Coulomb repulsion, this behavior is likely the result of counterion-induced as well as membrane-mediated attractions.