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We present the results of an extensive search for periodic and irregular variable pre-main sequence (PMS) stars in the young (2-4Myr) open cluster NGC 2264, based on photometric monitoring using the Wide Field Imager (WFI) on the 2.2m telescope on La Silla (Chile). In total, about 10600 stars with I_C magnitudes between 9.8mag and 21mag have been monitored in our 34'x33' field. Time series data were obtained in the I_C band in 44 nights between Dec. 2000 and March 2001; altogether we obtained 88 data points per star. Using two different time series analysis techniques (Scargle periodogram and CLEAN) we found 543 periodic variable stars with periods between 0.2 days and 15 days. Also, 484 irregular variable stars were identified using a χ²-test. In addition we have carried out nearly simultaneous observations in V, R_C and a narrow-band Hα filter. The photometric data enable us to reject background and foreground stars from our sample of variable stars according to their location in the I_C vs. (R_C-I_C) colour-magnitude and (R_C-Hα) vs. (R_C-I_C) colour-colour diagrams. We identified 405 periodic variable and 184 irregular variable PMS stars as cluster members using these two different tests. In addition 35 PMS stars for which no significant variability were detected could be identified as members using an Hα emission index criterion. This yields a total of 624 PMS stars in NGC 2264, of which only 182 were previously known. Most of the newly found PMS stars are fainter than I_C≃15mag and of late spectral type (>M2). We find that the periodic variables, as a group, have a smaller degree of variability and smaller Hα index than the irregular variables. This suggests that the sample of periodic variables is biased towards weak-line T Tauri stars (WTTSs) while most of the irregular variables are probably classical T Tauri stars (CTTSs). We have quantified this bias and estimated that the expected fraction of WTTSs among PMS stars in the cluster is 77%. This is relatively close to the fraction of WTTSs among the periodic variables which is 85%. We also estimated the total fraction of variables in the cluster using only two well selected concentrations of PMS stars called NGC 2264N & S in which we can easily estimate the total number of PMS stars. We find that at least 74% of the PMS stars in the cluster with I_C≤18.0mag were found to be variable (either periodic or irregular) by our study. This number shows that our search for PMS stars in NGC 2264 through extensive and accurate photometric monitoring is very efficient in detecting most PMS stars down to at least I_C=18.0mag.