A319 FLT CREW DEPARTING RWY 19L AT LAS REPORTS RWY INCURSION BY B737 CAUSING A REJECTED TKOF.

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THE SUBJECT OF THIS RPT IS A RWY INCURSION RESULTING IN A REJECTED TKOF. THE FO WAS PF DEPARTING RWY 19L IN LAS. TKOF PWR WAS REDUCED TO AN ASSUMED TEMP OF 48 DEGS C. AFTER CLRNC WAS RECEIVED THE TKOF ROLL BEGAN NORMALLY. ACCELERATING THROUGH APPROX 40 KTS I NOTICED AN ACFT TRAVELING DOWNFIELD ON A COURSE AND SPD THAT CAUSED ME TO SUSPECT IT WOULD CROSS OUR TKOF PATH. I COMMENTED TO THE FO (PF) 'I DON'T THINK HE'S GOING TO STOP.' THE FO AGREED. SHORTLY THEREAFTER THE OFFENDING ACFT CROSSED OUR PATH. WE SIMULTANEOUSLY ANNOUNCED THE INCURSION. I IMMEDIATELY ASSUMED ACFT CTL AND DISCONTINUED THE TKOF AT AN ESTIMATED SPD OF 50-60 KTS WITH THE FO SEAMLESSLY TRANSITIONING TO NON FLYING DUTIES. I ASSUMED ACFT CTL; SELECTED FULL REVERSE THRUST AND APPLIED MANUAL BRAKING TO REDUCE SPD AND AVOID A COLLISION. AFTER STOPPING CABIN ANNOUNCEMENT WAS MADE. AFTER EXITING RWY A SECOND CABIN ANNOUNCEMENT WAS MADE AND I SPOKE WITH THE FLT ATTENDANTS DIRECTLY VIA THE INTERPHONE. WE BRIEFLY REVIEWED THE SITUATION WITH ATC. THEY ASSURED US ONCE AGAIN WE HAD NOT COMMITTED AN ERROR. WHILE WAITING FOR THE BRAKES TO COOL; THE FO AND I REVIEWED THE POH AND FOM FOR GUIDANCE OF WHICH LITTLE WAS FOUND. I THEN CONTACTED MAINT AND DISPATCH DIRECTLY FOR A BRIEF DISCUSSION OF THE EVENT AND MY INTENTIONS TO PROCEED IF ALL PARTIES WERE IN AGREEMENT. AFTER CONSULTATIONS AND BRAKE COOLING WERE COMPLETED WE RETURNED TO THE RWY FOR TKOF AS ORIGINALLY SCHEDULED. IT IS UNCLR TO ME AT THIS TIME WHETHER THE ERROR CAUSING THE RWY INCURSION AND SUBSEQUENT REJECTED TKOF RESTS WITH THE LAS ATC FACILITY OR THE PLT OF THE XING ACFT. WE WERE ASSURED HOWEVER OUR FLT WAS ISSUED A VALID TKOF CLRNC.