Quantification of the dynamics of RNA metabolism is essential for understanding gene regulation in health and disease. Existing methods rely on metabolic labeling of nascent RNAs and physical separation or inference of labeling through PCR-generated mutations, followed by short-read sequencing. However, these methods are limited in their ability to identify transient decay intermediates or co-analyze RNA decay with cis-regulatory elements of RNA stability such as poly(A) tail length and modification status, at single molecule resolution. Here we use 5-ethynyl uridine (5EU) to label nascent RNA followed by direct RNA sequencing with nanopores. We developed RNAkinet, a deep convolutional and recurrent neural network that processes the electrical signal produced by nanopore sequencing to identify 5EU-labeled nascent RNA molecules. RNAkinet demonstrates generalizability to distinct cell types and organisms and reproducibly quantifies RNA kinetic parameters allowing the combined interrogation of RNA metabolism and cis-acting RNA regulatory elements.