Binds with high affinity to RNA molecules that contain AU-rich elements (AREs) found within the 3'-UTR of many proto-oncogenes and cytokine mRNAs. Also binds to double- and single-stranded DNA sequences in a specific manner and functions a transcription factor. Each of the RNA-binding domains specifically can bind solely to a single-stranded non-monotonous 5'-UUAG-3' sequence and also weaker to the single-stranded 5'-TTAGGG-3' telomeric DNA repeat. Binds RNA oligonucleotides with 5'-UUAGGG-3' repeats more tightly than the telomeric single-stranded DNA 5'-TTAGGG-3' repeats. Binding of RRM1 to DNA inhibits the formation of DNA quadruplex structure which may play a role in telomere elongation. May be involved in translationally coupled mRNA turnover. Implicated with other RNA-binding proteins in the cytoplasmic deadenylation/translational and decay interplay of the FOS mRNA mediated by the major coding-region determinant of instability (mCRD) domain. May play a role in the regulation of the rhythmic expression of circadian clock core genes. Directly binds to the 3'UTR of CRY1 mRNA and induces CRY1 rhythmic translation. May also be involved in the regulation of PER2 translation. Identified in a IGF2BP1-dependent mRNP granule complex containing untranslated mRNAs. Part of a complex associated with the FOS mCRD domain and consisting of PABPC1, PAIP1, CSDE1/UNR and SYNCRIP. Interacts with IGF2BP2. Interacts with GTPBP1. Interacts with EIF4G1; the interaction requires RNA. Interacts with EIF3B and RPS3. Localized in cytoplasmic mRNP granules containing untranslated mRNAs. Component of ribonucleosomes. Cytoplasmic localization oscillates diurnally. Arg-345 is dimethylated, probably to asymmetric dimethylarginine. Methylated by PRMT1, in an insulin-dependent manner. The PRMT1-mediated methylation regulates tyrosine phosphorylation (By similarity). Contaminating sequence. Sequence of unknown origin in the N-terminal part. Several sequence conflicts.