Air carrier Captain reported a ground conflict during takeoff when another aircraft crossed the hold short of the departing 737. Tower Controller issued an immediate stop order to the intruding aircraft as the 737 continued safely.

Narrative

As we were taxing out to Runway XXR at ZZZ; the ground controller made an enquiry to Aircraft Y behind us if they would be able to accept an intersection takeoff from Taxiway 1 for Runway XXR; the crew advised they could. We were handed to the tower and advised to taxi full length. Upon arriving at the departure end of Runway XXR; all checklists completed; Tower cleared us for Takeoff Runway XXR on the ZZZZZ RNAV Departure. Before entering the Runway; all takeoff lights were turned on; Runway identification and visual inspections of final approach and departure runway were confirmed. The aircraft was lined up on the runway; both engines stabilized and takeoff power set. As the aircraft accelerated; a CRJ 200 crossed the hold short line at Runway XXR Taxiway 1 and encroached upon Runway XXR. The Tower Controller issued an immediate stop order to the CRJ as we accelerated past them. The CRJ crew stated that they had been told to line up and wait Runway XXR; the Tower controller advised then that they had been told to Line Up and wait Runway XXR full length. A normal takeoff was completed with no further incident.