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Context. Continuum time delays from accretion disks in active galactic nuclei (AGN) has been proposed long time ago as a tool for measuring distances to the monitored sources. However, the method faces serious problems as a number of effects must be taken into account, including the contribution from the Broad Line Region (BLR). Aims. In this paper, we model the expected time delays when both the disk reprocessing of the incident X-ray flux and further reprocessing by the BLR are included, with the aim to see if the two effects can be disentangled. Methods. We use simple response function for the accretion disk, without relativistic effects, and we use a parametric description to account for the BLR contribution. We include only scattering of the disk emission by the BLR inter-cloud medium. We also use artificial lightcurves with 1-day sampling to check if the effects are likely to be seen in real data. Results. We show that the effect of the BLR scattering on the predicted time delay is very similar to the effect of rising height of the X-ray source, without any BLR contribution. This brings additional degeneracy if we want in the future to recover the parameters of the system from the observed time delays in a specific object. Both effects, however, modify the slope of the delay versus wavelength curve when plotted in log space which opens a way to obtaining bare disk time delay needed for cosmology. In addition, when the disk irradiation is strong, the modification of the predicted delay by the BLR scattering and by X-ray source height become considerably different. However, the required data quality must be high since our artificial curves with 1-day sampling give rather noisy results.