We report the synthesis and characterisation of polycrystalline Na$_2$RuO$_3$, a layered material in which the Ru$^{4+}$ ($4d^4$ configuration) form a honeycomb lattice. The optimal synthesis condition was found to produce a nearly ordered Na$_2$RuO$_3$ ($C2/c$ phase), as assessed from the refinement of the time-of-flight neutron powder diffraction. Magnetic susceptibility measurements reveal a large temperature-independent Pauli paramagnetism ($chi_0 sim 1.42(2)times10^{-3}$ emu/mol Oe) with no evidence of magnetic ordering down to 1.5 K, and with an absence of dynamic magnetic correlations, as evidenced by neutron scattering spectroscopy. The intrinsic susceptibility ($chi_0$) together with the Sommerfeld coeficient of $gamma=11.7(2)$ mJ/Ru mol K$^2$ estimated from heat capacity measurements, gives an enhanced Wilson ratio of $R_Wapprox8.9(1)$, suggesting that magnetic correlations may be present in this material. While transport measurements on pressed pellets show nonmetallic behaviour, photoemission spectrocopy indicate a small but finite density of states at the Fermi energy, suggesting that the bulk material is metallic. Except for resistivity measurements, which may have been compromised by near surface and interface effects, all other probes indicate that Na$_2$RuO$_3$ is a moderately correlated electron metal. Our results thus stand in contrast to earlier reports that Na$_2$RuO$_3$ is an antiferromagnetic insulator at low temperatures.
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