The duration of the Minimal Route Advertisement Interval (MRAI) and the implementation of MRAI timers have a significant influence on the convergence time of the Border Gateway Protocol (BGP). Previous studies have reported existence of optimal MRAI values that minimize the BGP convergence time for various network topologies and traffic loads. In this paper, we propose the adaptive MRAI algorithm for adaptive adjustment of MRAI values. We also introduce reusable MRAI timers that independently limit advertisements of individual destinations. The modified BGP is named BGP with adaptive MRAI (BGP-AM). BGP processing delay used in the evaluation of BGP-AM is based on reported measurements. ns-2 simulation results demonstrate that BGP-AM leads to a shorter convergence time while maintaining a number of update messages comparable to the current BGP implementation. BGP-AM convergence time depends linearly on the BGP processing delay.