Massively parallel reporter assays (MPRAs) enable nucleotide-resolution dissection of transcriptional regulatory regions, such as enhancers, but only few regions at a time. Here we present a combined experimental and computational approach, Systematic high-resolution activation and repression profiling with reporter tiling using MPRA (Sharpr-MPRA), that allows high-resolution analysis of thousands of regions simultaneously. Sharpr-MPRA combines dense tiling of overlapping MPRA constructs with a probabilistic graphical model to recognize functional regulatory nucleotides, and to distinguish activating and repressive nucleotides, using their inferred contribution to reporter gene expression. We used Sharpr-MPRA to test 4.6 million nucleotides spanning 15,000 putative regulatory regions tiled at 5-nucleotide resolution in two human cell types. Our results recovered known cell-type-specific regulatory motifs and evolutionarily conserved nucleotides, and distinguished known activating and repressive motifs. Our results also showed that endogenous chromatin state and DNA accessibility are both predictive of regulatory function in reporter assays, identified retroviral elements with activating roles, and uncovered 'attenuator' motifs with repressive roles in active chromatin.