Context. Temporal variability of narrow absorption lines in high-resolution spectra of Type Ia supernovae (SNe Ia) is studied to search for circumstellar matter. Time series which resolve the profiles of absorption lines such as Na I D or Ca II H&K are expected to reveal variations due to photoionisation and subsequent recombination of the gases. The presence, composition, and geometry of circumstellar matter may hint at the elusive progenitor system of SNe Ia and could also affect the observed reddening law. Aims. To date, there are few known cases of time-varying Na I D absorption in SNe Ia, all of which occurred during relatively late phases of the supernova (SN) evolution. Photoionisation, however, is predicted to occur during the early phases of SNe Ia, when the supernovae peak in the ultraviolet. We attempt, therefore, to observe early-time absorption-line variations by obtaining high-resolution spectra of SNe before maximum light. Methods. We have obtained photometry and high-resolution spectroscopy of SNe Ia 2013gh and iPTF 13dge, to search for absorption-line variations. Furthermore, we study interstellar absorption features in relation to the observed photometric colours of the SNe. Results. Both SNe display deep Na I D and Ca II H&K absorption features. Furthermore, small but significant variations are detected in a feature of the Na I D profile of SN 2013gh. The variations are consistent with either geometric effects of rapidly moving or patchy gas clouds or photoionisation of Na I gas at R ≈ 1019 cm from the explosion. Conclusions. Our analysis indicates that it is necessary to focus on early phases to detect photoionisation effects of gases in the circumstellar medium of SNe Ia. Different absorbers such as Na I and Ca II can be used to probe for matter at different distances from the SNe. The nondetection of variations during early phases makes it possible to put limits on the abundance of the species at those distances.