We report detailed experimental results on the magnetic susceptibility of high-quality ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystals for the applied magnetic field H parallel, ${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$, and perpendicular, ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}}$, to the c direction. The data were obtained from 5 to 300 K, and with ${\mathrm{\ensuremath{\mu}}}_{0}$H\ensuremath{\le}0.6 T, for which ${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$ and ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}}$ above the superconducting transition correspond to the so-called weak magnetic-field limit, even for reduced temperatures, \ensuremath{\varepsilon}\ensuremath{\equiv}(T-${\mathit{T}}_{\mathit{C}\mathit{O}}$)/${\mathit{T}}_{\mathit{C}\mathit{O}}$, of the order of \ensuremath{\varepsilon}=2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$, where ${\mathit{T}}_{\mathit{C}\mathit{O}}$ is the mean-field-like normal-superconducting transition temperature. For T>${\mathit{T}}_{\mathit{C}\mathit{O}}$, ${\mathrm{\ensuremath{\chi}}}_{\mathit{c}}$ is found to be temperature independent and its average value for the samples measured here is (2.7\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$. In contrast, ${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$(T) is found to be temperature independent, and equal to (5.2\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$, only above T-${\mathit{T}}_{\mathit{C}\mathit{O}}$\ensuremath{\approxeq}25 K and up to the highest temperature studied here (300 K). Between ${\mathit{T}}_{\mathit{C}\mathit{O}}$ and T-${\mathit{T}}_{\mathit{C}\mathit{O}}$\ensuremath{\approxeq}25 K, ${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$(T) is appreciably rounded. The excess diamagnetism above but near ${\mathit{T}}_{\mathit{C}\mathit{O}}$, for H parallel to the c axis, \ensuremath{\Delta}${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$, is analyzed in terms of the existing approaches for independent Gaussian fluctuations of the superconducting-order-parameter amplitude in layered materials and also compared with the paraconductivity measured in the same samples.The so-called mean-field-like region will correspond to, approximately, ${10}^{\mathrm{\ensuremath{-}}2}$\ensuremath{\lesssim}\ensuremath{\varepsilon}\ensuremath{\lesssim}0.15. Beyond the lower \ensuremath{\varepsilon} limit, closer to ${\mathit{T}}_{\mathit{C}\mathit{O}}$, both the paraconductivity and \ensuremath{\Delta}${\mathrm{\ensuremath{\chi}}}_{\mathit{a}\mathit{b}}$(\ensuremath{\varepsilon}) separate from the mean-field region behavior. Although so close to the transition we cannot exclude the influence of small stoichiometric inhomogeneities, these data for \ensuremath{\varepsilon}\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}2}$ may be explained on the grounds of the three-dimensional XY model, with a critical exponent of x=-1/3 for the paraconductivity and x=-2/3 for the fluctuation-induced diamagnetism. A scenario compatible with the experimental results is characterized by the values of the correlation length amplitude in the ab plane and in the c direction of, respectively, ${\ensuremath{\xi}}_{\mathit{a}\mathit{b}}$(0)=(1.1\ifmmode\pm\else\textpm\fi{}0.2) nm and ${\ensuremath{\xi}}_{\mathit{c}}$(0)=(0.12\ifmmode\pm\else\textpm\fi{}0.02) nm, two Josephson coupled superconducting planes in the unit-cell length, and a complex order parameter with two real components, i.e., conventional $^{1}$${\mathit{s}}_{0}$-wave pairing or one-complex-component unconventional pairing.