Transcription factors (TFs) can relay signals through temporal alterations in their levels. The cell stress responsive TF p53 exhibits different dynamics depending on the type of stress, which influence the magnitude and dynamics of expression of its target genes and subsequent cellular outcomes. The mechanisms decoding p53 dynamics into levels and dynamics of RNA and protein of its targets remain unclear. We systematically quantified p53 target mRNA and protein levels over time under two p53 dynamical regimes – oscillatory and sustained – using RNA-seq and quantitative mass spectrometry. We categorized the mRNA dynamical patterns arising from oscillatory or sustained p53 expression, as well as the corresponding protein dynamics. We found that in both cases oscillatory dynamics allowed for the greatest variety of dynamical patterns of the downstream species. Target proteins from a wide range of functional categories were induced under both p53 dynamic conditions, with induction levels being overall higher under sustained dynamics. Mathematical modeling combined with analysis of empirical data revealed three mechanisms of decoding p53 dynamics: adjustment of mRNA and protein degradation rates, adjustment of activation thresholds for expression of mRNA and corresponding protein levels, and usage of coherent and incoherent feed-forward loop motifs in generating exclusive responses to p53 oscillatory or sustained dynamics, respectively. Our results highlight the diversity of mechanisms that decode complex TF dynamics into dynamical patterns of mRNA and proteins.