We calculate the response of a line emitted from a relativisic accretion disc to a continuum variation of the central illuminating source. This model might be relevant to the very broad and sometimes redshifted emission lines that have been observed at optical and X-ray energies in active galactic nuclei and X-ray binaries. We consider separately the cases of point-like and extended central sources. Based on the first three moments of the line energy distribution (i.e. the line intensity, centroid energy and width) and the two-dimensional transfer function, we identify a number of characteristic features, which can help in assessing the presence of a relativistic accretion disc and in estimating its parameters. In particular, by combining an absolute time measurement of the maximum of the line response function with a relative measurement in units of light crossing time, the mass of the central object can be derived.