The mechanisms by which neural circuits generate an extensible library of motor motifs and flexibly string them into arbitrary sequences are unclear. We developed a model in which inhibitory basal ganglia output neurons project to thalamic units that are themselves bidirectionally connected to a recurrent cortical network. During movement sequences, electrophysiological recordings of basal ganglia output neurons show sustained activity patterns that switch at the boundaries between motifs. Thus, we model these inhibitory patterns as silencing some thalamic neurons while leaving others disinhibited and free to interact with cortex during specific motifs. We show that a small number of disinhibited thalamic neurons can control cortical dynamics to generate specific motor output in a noise robust way. If the thalamic units associated with each motif are segregated, many motor outputs can be learned without interference and then combined in arbitrary orders for the flexible production of long and complex motor sequences.