  Twisted deformations of the conformal symmetry in the Hopf algebraic
framework are constructed. The first one is obtained by a Jordanian twist built
up from dilatation and momenta generators. The second is the light-like
$\kappa$-deformation of the Poincare algebra extended to the conformal algebra,
obtained by a twist corresponding to the extended Jordanian r-matrix. The
$\kappa$-Minkowski spacetime is covariant quantum space under both of these
deformations. The extension of the conformal algebra by the noncommutative
coordinates is presented in two cases. The differential realizations for
$\kappa$-Minkowski coordinates, as well as their left-right dual counterparts,
are also included.
