  The integral parameters of neutron stars are studied taking into account the
hadron-quark phase transition, which leads to the formation of a core of quark
matter in the central part of a star. The quark matter is described using the
local Nambu - Jona-Lasinio (NJL) model. The thermodynamic characteristics of
the hadron matter are calculated in the framework of an extended version of the
relativistic mean field (RMF) model that includes the contribution of the
scalar-isovector $\delta$-meson effective field. A Maxwell construction is used
to determine the parameters of the phase transition. It is shown that for the
equation of state examined here, stable hybrid stars correspond to a narrow
range of values for the central density. In our model hybrid stars lie on the
same branch as neutron stars, so that a branch with a third family is not
formed. It is shown that for the equation of state examined here, stable hybrid
stars correspond to a narrow range of values for the central density
$\rho_c\in(1.71 \div 1.73]\cdot 10^{15}$ g/cm$^3$. In our model hybrid stars
lie on the same branch as neutron stars, so that a branch with a third family
is not formed. The maximum mass of a stable hybrid star is found to be $M_{max}
= 2.05 M_\odot$. The configuration with the maximum mass has a quark core with
mass $M_{core} \approx 10^{-3} M_\odot$ and radius $R_{core} \approx 0.6$ km.
