The functional organization of eukaryotic genomes correlates with specific patterns of histone methylations. Regulatory regions in genomes such as enhancers and promoters differ in their extent of methylation of histone H3 at lysine-4 (H3K4), but it is largely unknown how the different methylation states are specified and controlled. Here, we show that the Kdm5c/Jarid1c/SMCX member of the Kdm5 family of H3K4 demethylases can be recruited to both enhancer and promoter elements in mouse embryonic stem cells and in neuronal progenitor cells. Knockdown of Kdm5c deregulates transcription via local increases in H3K4me3. Our data indicate that by restricting H3K4me3 modification at core promoters, Kdm5c dampens transcription, but at enhancers Kdm5c stimulates their activity. Remarkably, an impaired enhancer function activates the intrinsic promoter activity of Kdm5c-bound distal elements. Our results demonstrate that the Kdm5c demethylase plays a crucial and dynamic role in the functional discrimination between enhancers and core promoters. Display omitted ► The H3K4me3/2 demethylase Kdm5c interacts with gene-specific transcription factors ► Genomic profiles of Kdm5c in ESCs reveal promoter-proximal and -distal binding ► Kdm5c represses promoter activity but stimulates enhancer function ► Dynamic H3K4me3/2 thus modulates promoter and enhancer function Regulatory regions of eukaryotic genomes such as enhancers and promoters differ in their extent of methylation of histone H3 at lysine 4 (H3K4). Using embryonic stem cells, Timmers and colleagues report that the Kdm5c/Jarid1c/SMCX demethylase controls H3K4 mono- and trimethylation with different transcriptional outcomes. At promoters, Kdm5c dampens transcription, but at enhancers, Kdm5c stimulates their activity. Impairment of enhancer function activates an intrinsic promoter activity of Kdm5c sites. This demonstrates that Kdm5c plays a dynamic role in the functional discrimination between genomic elements.