Results. M68 had 45 previously confirmed variables, including 42 RRL and 2 SX Phoenicis (SX Phe) stars. In this paper we determine new periods and search for new variables, especially in the core of the cluster where our method performs particularly well. We detect 4 additional SX Phe stars and confirm the variability of another star, bringing the total number of confirmed variable stars in this cluster to 50. We also used archival data stretching back to 1951 to derive period changes for some of the single-mode RRL stars, and analyse the significant number of double-mode RRL stars in M68. Furthermore, we find evidence for double-mode pulsation in one of the SX Phe stars in this cluster. Using the different classes of variables, we derived values for the metallicity of the cluster of [Fe/H] = -2.07 +/- 0.06 on the ZW scale, or -2.20 +/- 0.10 on the UVES scale, and found true distance moduli mu(0) = 15.00 +/- 0.11 mag (using RR0 stars), 15.00 +/- 0.05 mag (using RR1 stars), 14.97 +/- 0.11 mag (using SX Phe stars), and 15.00 +/- 0.07 mag (using the M-V-[Fe/H] relation for RRL stars), corresponding to physical distances of 10.00 +/- 0.49, 9.99 +/- 0.21, 9.84 +/- 0.50, and 10.00 +/- 0.30 kpc, respectively. Thanks to the first use of difference image analysis on time-series observations of M 68, we are now confident that we have a complete census of the RRL stars in this cluster.