  We present measurements of $e^+e^-$ production at midrapidity in Au$+$Au
collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV. The invariant yield is studied
within the PHENIX detector acceptance over a wide range of mass ($m_{ee} <$ 5
GeV/$c^2$) and pair transverse momentum ($p_T$ $<$ 5 GeV/$c$), for minimum bias
and for five centrality classes. The \ee yield is compared to the expectations
from known sources. In the low-mass region ($m_{ee}=0.30$--0.76 GeV/$c^2$)
there is an enhancement that increases with centrality and is distributed over
the entire pair \pt range measured. It is significantly smaller than previously
reported by the PHENIX experiment and amounts to $2.3\pm0.4({\rm
stat})\pm0.4({\rm syst})\pm0.2^{\rm model}$ or to $1.7\pm0.3({\rm
stat})\pm0.3({\rm syst})\pm0.2^{\rm model}$ for minimum bias collisions when
the open-heavy-flavor contribution is calculated with {\sc pythia} or {\sc
mc@nlo}, respectively. The inclusive mass and $p_T$ distributions as well as
the centrality dependence are well reproduced by model calculations where the
enhancement mainly originates from the melting of the $\rho$ meson resonance as
the system approaches chiral symmetry restoration. In the intermediate-mass
region ($m_{ee}$ = 1.2--2.8 GeV/$c^2$), the data hint at a significant
contribution in addition to the yield from the semileptonic decays of
heavy-flavor mesons.
