We describe a point-set registration algorithm based on a novel free point transformer (FPT) network, designed for points extracted from multimodal biomedical images for registration tasks, such as those frequently encountered in ultrasound-guided interventional procedures. FPT is constructed with a global feature extractor which accepts unordered source and target point-sets of variable size. The extracted features are conditioned by a shared multilayer perceptron point transformer module to predict a displacement vector for each source point, transforming it into the target space. The point transformer module assumes no vicinity or smoothness in predicting spatial transformation and, together with the global feature extractor, is trained in a data-driven fashion with an unsupervised loss function. In a multimodal registration task using prostate MR and sparsely acquired ultrasound images, FPT yields comparable or improved results over other rigid and non-rigid registration methods. This demonstrates the versatility of FPT to learn registration directly from real, clinical training data and to generalize to a challenging task, such as the interventional application presented.