The evolution of the electronic structure and magnetic properties with Co substitution for Fe in the solid solution Fe$_{1-x}$Co$_x$Ga$_3$ was studied by means of electrical resistivity, magnetization, ab-initio band structure calculations, and nuclear spin-lattice relaxation $1/T_1$ of the $^{69,71}$Ga nuclei. Temperature dependencies of the electrical resistivity reveal that the evolution from the semiconducting to the metallic state in the Fe$_{1-x}$Co$_x$Ga$_3$ system occurs at $0.025<x<0.075$. The $^{69,71}(1/T_1)$ was studied as a function of temperature in a wide temperature range of $2!-!300$ K for the concentrations $x = 0.0,$ $0.5,$ and $1.0$. In the parent semiconducting compound FeGa$_3$, the temperature dependence of the $^{69}(1/T_1)$ exhibits a huge maximum at about $T!sim!6$ K indicating the existence of in-gap states. The opposite binary compound, CoGa$_3$, demonstrates a metallic Korringa behavior with $1/T_1$ $propto T$. In Fe$_{0.5}$Co$_{0.5}$Ga$_3$, the relaxation is strongly enhanced due to spin fluctuations and follows $1/T_1propto T^{1/2}$, which is a unique feature of weakly and nearly antiferromagnetic metals. This itinerant antiferromagnetic behavior contrasts with both magnetization measurements, showing localized magnetism with a relatively low effective moment of about 0.7 $mu_B$/f.u., and ab initio band structure calculations, where a ferromagnetic state with an ordered moment of 0.5 $mu_B$/f.u. is predicted. The results are discussed in terms of the interplay betwen the localized and itinerant magnetizm including in-gap states and spin fluctuations.
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