Multiple sequence alignments (MSAs) are used for structural^, and evolutionary predictions^,, but the complexity of aligning large datasets requires the use of approximate solutions, including the progressive algorithm. Progressive MSA methods start by aligning the most similar sequences and subsequently incorporate the remaining sequences, from leaf to root, based on a guide tree. Their accuracy declines substantially as the number of sequences is scaled up. We introduce a regressive algorithm that enables MSA of up to 1.4 million sequences on a standard workstation and substantially improves accuracy on datasets larger than 10,000 sequences. Our regressive algorithm works the other way around from the progressive algorithm and begins by aligning the most dissimilar sequences. It uses an efficient divide-and-conquer strategy to run third-party alignment methods in linear time, regardless of their original complexity. Our approach will enable analyses of extremely large genomic datasets such as the recently announced Earth BioGenome Project, which comprises 1.5 million eukaryotic genomes.