Eukaryotic cells contain a variety of RNA-protein macrocomplexes termed RNP granules. Different types of granules share multiple protein components; however, the crosstalk between spatially separated granules remains unaddressed. Paraspeckles and stress granules (SGs) are prototypical RNP granules localized exclusively in the nucleus and cytoplasm, respectively. Both granules are implicated in human diseases, such as amyotrophic lateral sclerosis. We characterized the composition of affinity-purified paraspeckle-like structures and found a significant overlap between the proteomes of paraspeckles and SGs. We further show that paraspeckle hyperassembly is typical for cells subjected to SG-inducing stresses. Using chemical and genetic disruption of SGs, we demonstrate that formation of microscopically visible SGs is required to trigger and maintain stress-induced paraspeckle assembly. Mechanistically, SGs may sequester negative regulators of paraspeckle formation, such as UBAP2L, alleviating their inhibitory effect on paraspeckles. Our study reveals a novel function for SGs as positive regulators of nuclear RNP granule assembly and suggests a role for disturbed SG-paraspeckle crosstalk in human disease.