  Muons created by $\nu_\mu$ charged current (CC) interactions in the water
surrounding the ANTARES neutrino telescope have been almost exclusively used so
far in searches for cosmic neutrino sources. Due to their long range, highly
energetic muons inducing Cherenkov radiation in the water are reconstructed
with dedicated algorithms that allow the determination of the parent neutrino
direction with a median angular resolution of about \unit{0.4}{\degree} for an
$E^{-2}$ neutrino spectrum. In this paper, an algorithm optimised for accurate
reconstruction of energy and direction of shower events in the ANTARES detector
is presented. Hadronic showers of electrically charged particles are produced
by the disintegration of the nucleus both in CC and neutral current (NC)
interactions of neutrinos in water. In addition, electromagnetic showers result
from the CC interactions of electron neutrinos while the decay of a tau lepton
produced in $\nu_\tau$ CC interactions will in most cases lead to either a
hadronic or an electromagnetic shower. A shower can be approximated as a point
source of photons. With the presented method, the shower position is
reconstructed with a precision of about \unit{1}{\metre}, the neutrino
direction is reconstructed with a median angular resolution between
\unit{2}{\degree} and \unit{3}{\degree} in the energy range of
\SIrange{1}{1000}{TeV}. In this energy interval, the uncertainty on the
reconstructed neutrino energy is about \SIrange{5}{10}{\%}. The increase in the
detector sensitivity due to the use of additional information from shower
events in the searches for a cosmic neutrino flux is also presented.
