Using sequence profile methods and structural comparisons we characterize a previously unknown family of nucleic acid polymerases in a group of mobile elements from genomes of diverse bacteria, an algal plastid and certain DNA viruses, including the recently reported Sputnik virus. Using contextual information from domain architectures and gene-neighborhoods we present evidence that they are likely to possess both primase and DNA polymerase activity, comparable to the previously reported prim-pol proteins. These newly identified polymerases help in defining the minimal functional core of superfamily A DNA polymerases and related RNA polymerases. Thus, they provide a framework to understand the emergence of both DNA and RNA polymerization activity in this class of enzymes. They also provide evidence that enigmatic DNA viruses, such as Sputnik, might have emerged from mobile elements coding these polymerases.