I know that you can use nice to re assign priorities of processes but which tool can be used to configure the CPU priority of a process ?
Try the control groups (cgroups) facility. Introduced since Linux 2.6.24, it is a very flexible tool to assign CPU shares to processes as well as to place caps on resource (blockio, network, memory) utilization for each process. Here's documentation.
Use the command "renice" to change a process priority