The fluctuation-induced diamagnetism of underdoped high-temperature superco
nductors is studied in the framework of the Lawrence-Doniach model. By taki
ng into account the fluctuations of the phase of the order parameter only,
the latter reduces to a layered XY model describing a liquid of vortices th
at can be either thermally excited or induced by the external magnetic held
. The diamagnetic response is given by a current-current correlation functi
on that is evaluated using the Coulomb-gas analogy. Our results are then ap
plied to recent measurements of fluctuation diamagnetism in underdoped YBa2
Cu3O6.67. They make possible the understanding of both the observed anomalo
us temperature dependence of the zero-field susceptibility and the two dist
inct regimes appearing in the magnetic-field dependence of the magnetizatio
n.