Interbreeding between modern humans and archaic hominins has contributed to the genomes of present-day human populations. Introgressed archaic variants are not uniformly distributed throughout the genome, but are enriched in regulatory regions, particularly in enhancers active in immune cell types, suggesting they have the potential to contribute to gene regulation and organism-level traits. However, due to the lack of diversity in genomic databases, research on the impacts of archaic introgression has focused mainly on the Neanderthal variants present in European populations, to the detriment of our understanding of the Neanderthal and Denisovan variants present in the rest of the world. Using a Massively Parallel Reporter Assay, we functionally characterise the regulatory activity of over 26,000 Denisovan and Neanderthal variants present in modern-day Papuan populations. We quantify the regulatory activity of these archaic variants, and their non-archaic counterparts, in three cell lines of different genetic backgrounds. We identify Denisova and Neanderthal alleles that are capable of driving gene expression, which are predicted to regulate genes involved in immune cell processes, inflammation and wound healing, and facial and skeletal morphology. We additionally identify differentially active SNPs for which the archaic and non-archaic allele drive significantly different reporter gene expression. Differentially active SNPs are predicted to disrupt transcription factor binding sites and overlap known eQTLs. Many differentially active SNPs are predicted to regulate immune related genes, including a Denisovan SNP predicted to regulate TNFAIP3, a key regulator of immune and inflammatory signalling that has previously been identified as a target of archaic introgression. This work provides insight into the regulatory activity of archaic variants in Island Southeast Asia and, more broadly, the contribution of archaic introgression in shaping modern human genetic diversity.