A method is disclosed for providing prioritized routing table convergence in Border Gateway Protocol (BGP) hosts, as part of a BGP process that is executed by a route processor in a network, wherein the processor hosts a plurality of BGP routing tables each associated with a specified sub-address family (SAFI). A convergence priority order value is created and stored in association with each routing table. As part of performing a convergence phase of BGP processing, the convergence priority order value of each routing table is obtained. The convergence phase is then performed for the routing tables only according to an order that is represented by the convergence priority order values. Therefore, convergence proceeds more quickly and values needed by other routing processes become available earlier.