GA CL65 FLC REJECT TKOF TEB RWY 24 WHEN OBSERVING GLF4 LNDG ON RWY 19.

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I WAS THE PIC ON A CL65-100. THE FO WAS FLYING FROM THE L SEAT ON THE LEG FROM TEB TO CMH. WE TAXIED OUT OF GATE AND WERE INSTRUCTED BY GND CTL TO TAXI N ON TXWY P AND TO HOLD SHORT OF TXWY B. BEFORE WE ARRIVED AT TXWY B; THE GND CTLR INSTRUCTED US TO TAXI UP AND HOLD SHORT OF RWY 19. AFTER HOLDING SHORT OF RWY 19 FOR A MIN OR TWO; THE GND CTLR THEN INSTRUCTED US TO CROSS RWY 19 AND PULL INTO THE HOLDING APRON FOR RWY 24 AND MONITOR TWR FREQ. WE PULLED INTO THE HOLDING AREA BEHIND A GULFSTREAM 4 AND A CHALLENGER 604. THE CHKLISTS WERE COMPLETED TO THE POINT OF TAKING THE RWY. WE SAT AND WAITED AS THE TWR FIRST CLRED A CHALLENGER TO TAKE OFF RWY 19. THEN TWR CLRED A DORNIER 328 TO TAKE OFF ON RWY 24 AS HE HAD JUST TAXIED ACROSS RWY 19 BEHIND US. NEXT THE TWR CLRED THE CHALLENGER 604 IN FRONT OF US INTO POS AND HOLD ON RWY 24. THE CHALLENGER THEN WAS CLRED TO TAKE OFF. AFTER 3 MINS; THE GULFSTREAM 4 IN FRONT OF US WAS CLRED TO TAKE OFF FROM THAT POS ON RWY 24. AFTER ANOTHER 2 OR 3 MINS; THE TWR CLRED US TO TAKE OFF ON RWY 24; ALSO FROM THE HOLDING APRON. WHILE TAXIING INTO AND ALIGNING WITH THE RWY; THE BEFORE TKOF ITEMS ON THE CHKLIST WERE COMPLETED. THE FO THEN ADVANCED THE PWR AND CALLED TO SET THE THRUST ON THE ENGS. I COMPLETED SETTING THE PWR AND CALLED 'THRUST SET.' WHEN I LOOKED UP I NOTICED A GULFSTREAM 4 OUT OF THE R SIDE WINDOW THAT APPEARED TO BE LNDG ON RWY 19. I IMMEDIATELY CALLED FOR THE FO TO 'ABORT;' AND HE REDUCED THE THRUST LEVERS AND APPLIED THE BRAKES. I THEN CALLED THE TWR AND SAID THAT WE WERE ABORTING ON RWY 24; AS WE WATCHED THE GULFSTREAM 4 LNDG ON RWY 19 IN FRONT OF US. WE HAD ONLY REACHED ABOUT 40-50 KIAS; SO IT WAS A RELATIVELY MILD ABORT SEQUENCE. I THEN ASKED THE TWR CTLR TO CONFIRM THAT HE HAD CLRED US TO TAKE OFF AND HE CONFIRMED THAT HE HAD. THE TWR CTLR THEN EXPLAINED THAT HE WOULD HAVE INSTRUCTED THE GULFSTREAM TO GO AROUND; EXCEPT THAT HE HAD NOTICED THAT WE HAD ABORTED OUR TKOF FIRST. THE TWR CTLR THEN INSTRUCTED US TO BACK TAXI ON RWY 19 BACK TO THE HOLDING APRON FOR RWY 24. WE WERE THEN INSTRUCTED TO TAXI INTO POS AND HOLD ON RWY 24 AND THAT A DEHAVILLAND DASH 8 WAS LNDG ON RWY 19. AFTER THE DASH 8 CLRED THE INTXN; TWR THEN CLRED US TO TAKE OFF ON RWY 24. AFTER TKOF; THE TWR CTLR TOLD US TO CONTACT NEW YORK DEP AND APOLOGIZED FOR US HAVING TO ABORT OUR FIRST TKOF. I THEN CONTACTED NEW YORK DEP AND CONTINUED OUR FLT TO CMH. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR IS A FREQUENT FLYER INTO TEB. SINCE THIS INCIDENT; TWR NO LONGER ISSUES A TKOF CLRNC FROM THE STAGING AREA; AS IN THIS EVENT; BUT NOW ISSUES A 'POS AND HOLD' CLRNC FIRST.