We report the structure, magnetic, and thermal property measurements on single crystalline and polycrystalline samples of Ru substituted honeycomb lattice iridate Na2IrxRu1−xO3 (x = 0, 0.05, 0.1, 0.15, 0.2, 0.3, 0.5). The evolution of magnetism in Na2IrxRu1−xO3 has been studied using dc and ac magnetic susceptibility, and heat capacity measurements. The parent compound Na2IrO3 is a spin-orbit driven Mott insulator with magnetic order of reduced moments below TN = 15 K. In the Ru substituted samples the antiferromagnetic long range state is replaced by a spin glass like state even for the smallest substitution suggesting that the magnetic order in Na2IrO3 is extremely fragile. We argue that these behaviors indicate the importance of nearest-neighbor magnetic exchange in the parent Na2IrO3. Additionally, all samples show insulating electrical transport.