For higher Ru concentration ($x\ge 0.3$), the predominant $G$-type ordering is preserved along the $y$ axis while an $A$-type component is developed along the $x$ axis and its intensity increases as Ru content does. This component is characterized by a ferromagnetic ordering in the $a$ direction of one of the $\mathrm{Mn}\left(\mathrm{Ru}\right)O_6$ layers, coupled antiferromagnetically with the neighbor $\mathrm{Mn}\left(\mathrm{Ru}\right)O_6$ layer within the same bilayer. The study of the macroscopic magnetic properties shows that ferromagneticlike correlations are enhanced with increasing Ru content as deduced from the shift to higher temperature of the onset of the magnetic transition temperature. The magnetic transitions take place in two steps. At higher temperatures (140–200 K), short-range magnetic correlations are established. Tiny spontaneous magnetization is observed in the hysteresis loops with small coercive field. At $T_N\approx 115–125K$, long-range antiferromagnetic ordering is developed. The ferromagnetic component remains with a strong increase of coercivity. We discuss in the paper the possible origins of this ferromagnetic contribution.