$^{199}\mathrm{Hg}$ NMR measurements have been performed both in the normal and in the superconducting state for an oriented ${\mathrm{HgBa}}_{2}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$ superconducting powder sample with ${\mathit{T}}_{\mathit{c}}$=96 K. The large anisotropic Knight shift of $^{199}\mathrm{Hg}$, $^{199}$${\mathit{K}}_{\mathrm{ax}}$=-0.15% at room temperature, is explained by the chemical shift related to the linear Hg-O(2) bonding configuration. Both $^{199}$${\mathit{K}}_{\mathrm{iso}}$ and $^{199}$${\mathit{K}}_{\mathrm{ax}}$ decrease below ${\mathit{T}}_{\mathit{c}}$ and scale linearly with each other in the whole temperature range investigated. The $^{199}\mathrm{Hg}$ Knight shift $^{199}$K slowly decreases with decreasing temperature on approaching ${\mathit{T}}_{\mathit{c}}$ in the normal state, reflecting the decrease of the uniform spin susceptibility \ensuremath{\chi}\ensuremath{'}(0,0) with lowering temperature. The $^{199}\mathrm{Hg}$ spin-echo decay can be fit by the product of a Gaussian component (${\mathit{T}}_{\mathit{G}}^{\mathrm{\ensuremath{-}}1}$) and an exponential one (${\mathit{T}}_{\mathit{L}}^{\mathrm{\ensuremath{-}}1}$). The Gaussian component ${\mathit{T}}_{\mathit{G}}^{\mathrm{\ensuremath{-}}1}$ which is dominant above ${\mathit{T}}_{\mathit{c}}$, is shown to be due mainly to an indirect nuclear interaction via the conduction electrons (holes) and is found to be directly proportional to the spin contribution ${(}^{199}$${\mathit{K}}^{\mathrm{sp}}$) of the Knight shift. The exponential component ${\mathit{T}}_{\mathit{L}}^{\mathrm{\ensuremath{-}}1}$ becomes dominant well below ${\mathit{T}}_{\mathit{c}}$ and is ascribed to the effect of thermal motion of flux lines. The $^{199}\mathrm{Hg}$ nuclear spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ in the normal state shows a Korringa behavior well above ${\mathit{T}}_{\mathit{c}}$ with (${\mathit{T}}_{1}$T${)}^{\mathrm{\ensuremath{-}}1}$=0.1 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}1}$. Reduction of (${\mathit{T}}_{1}$T${)}^{\mathrm{\ensuremath{-}}1}$ with decreasing temperature is observed starting about 10 K above ${\mathit{T}}_{\mathit{c}}$ and is consistent with the decrease of \ensuremath{\chi}\ensuremath{'}(0,0) in the normal state observed in K(T) and ${\mathit{T}}_{\mathit{G}}^{\mathrm{\ensuremath{-}}1}$. $^{199}$${\mathit{K}}^{\mathrm{sp}}$(T) was extracted using the Korringa relation and below ${\mathit{T}}_{\mathit{c}}$, is found to fit the d-wave pairing scheme with a superconducting gap parameter 2${\mathrm{\ensuremath{\Delta}}}_{0}$=3.5${\mathit{k}}_{\mathit{BT}\mathit{c}}$. The d-wave pairing is also supported by the temperature dependence of $^{199}\mathrm{Hg}$ ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ in the superconducting state. The $^{63}\mathrm{Cu}$ ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ and ${\mathit{T}}_{2}^{\mathrm{\ensuremath{-}}1}$ measurements have been performed in the normal state. In contrast to the Korringa behavior of $^{199}\mathrm{Hg}$ ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ in the normal state, the preliminary results show the increase of the $^{63}\mathrm{Cu}$ (${\mathit{T}}_{1}$T${)}^{\mathrm{\ensuremath{-}}1}$ with decreasing temperature, indicating the enhancement of the antiferromagnetic fluctuations of ${\mathrm{Cu}}^{2+}$ moments common in the high-${\mathit{T}}_{\mathit{c}}$ cuprates. The reduction of $^{63}\mathrm{Cu}$ (${\mathit{T}}_{1}$T${)}^{\mathrm{\ensuremath{-}}1}$ is observed starting above ${\mathit{T}}_{\mathit{c}}$ and is compared with the decrease of $^{199}\mathrm{Hg}$ ${\mathit{K}}^{\mathrm{sp}}$, ${\mathit{T}}_{\mathit{G}}^{\mathrm{\ensuremath{-}}1}$, and (${\mathit{T}}_{1}$T${)}^{\mathrm{\ensuremath{-}}1}$ in the normal state. The $^{63}\mathrm{Cu}$ nuclear spin-spin relaxation ${\mathit{T}}_{2}^{\mathrm{\ensuremath{-}}1}$ is found to follow an exponential decay in the normal state and to decrease with decreasing temperature similar to the $^{199}\mathrm{Hg}$ ${\mathit{K}}^{\mathrm{sp}}$ and ${\mathit{T}}_{\mathit{G}}^{\mathrm{\ensuremath{-}}1}$. \textcopyright{} 1996 The American Physical Society.