Within the core of the MPLS network the P routers don't run BGP.
In fact that is one of the big advantages from an SP perspective.
So an IGP is run between the PE router's MPLS enabled interfaces and the P routers so that labels can be exchanged which ensure full reachability within the MPLS network.
Thank You Jon.... What I want to exactly ask is, Is it technically possible to achieve MPLS connectivity without IGP? Correct me if I am wrong or missing something.
It will be difficult to have fully mesh BGP between PE routers in MPLS network. A single pop itself may have 2 or more PE routers and just for forming neighborship it will be difficult spare interfaces.
P routers in MPLS make things easier and will have NLRI informations to any PE routers.
To make things more easier you can also use RR which can be at certain locations and through P routers you can have the Reachbility easily.