More than 200 extrasolar planets have been discovered around relatively nearby stars, primarily through the Doppler line shifts owing to reflex motions of their host stars, and more recently through transits of some planets across the faces of the host stars. The detection of planets with the shortest known periods, 1.2-2.5 days, has mainly resulted from transit surveys which have generally targeted stars more massive than 0.75 M(o), where M(o) is the mass of the Sun. Here we report the results from a planetary transit search performed in a rich stellar field towards the Galactic bulge. We discovered 16 candidates with orbital periods between 0.4 and 4.2 days, five of which orbit stars of masses in the range 0.44-0.75 M(o). In two cases, radial-velocity measurements support the planetary nature of the companions. Five candidates have orbital periods below 1.0 day, constituting a new class of ultra-short-period planets, which occur only around stars of less than 0.88 M(o). This indicates that those orbiting very close to more-luminous stars might be evaporatively destroyed or that jovian planets around stars of lower mass might migrate to smaller radii.