OPERROR LTSS WHEN SMALL COMMUTER CROSSES RWY 22R WHILE AN A300 IS ON TKOF ROLL. PF; FO; STATED REJECT. CAPT OBSERVED THE ACFT EXIT THE RWY AND CONTINUED TKOF.

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ON TKOF ROLL A SMALL COMMUTER CROSSED RWY 22R IN OUR TKOF PATH. THE INCURSION WAS ABOUT 8000 FT DOWN RWY 22R. THE FO WAS MAKING THE TKOF. I WAS HEAD DOWN MAKING PWR ADJUSTMENTS. THE FO STATED 'REJECT.' I WAS TEMPORARILY DISTR LOOKING AT ENG INSTS FOR SIGNS OF THE PROB. SEEING NO APPARENT PROB; I FINALLY LOOKED UP AND SAW THE SMALL COMMUTER XING DOWNFIELD ABOUT 6000 FT FROM OUR POS. AS THE OTHER ACFT WAS EXITING THE RWY I ELECTED TO CONTINUE THE TKOF. THE REMAINDER OF THE FLT WAS UNEVENTFUL. THIS WAS THE FIRST TIME THIS SIT HAS OCCURRED FOR EITHER PLT. IT HAD A VERY STARTLING EFFECT ON BOTH OF US. I NEED TO ADDRESS SEVERAL SPECIFIC CONCERNS. 1) THE FO SHOULD HAVE BEEN MORE SPECIFIC IN HIS REJECT CALL. HE KNEW WHAT WAS HAPPENING BUT I DID NOT. I WAS LOOKING FOR OTHER PROBS. 2) I SHOULD HAVE BEEN MORE COMMUNICATIVE IN ADVISING HIM TO CONTINUE THE TKOF. HE DID NOT BELIEVE THAT COURSE OF ACTION WAS UNSAFE BUT WANTED TO PURSUE THE MOST CONSERVATIVE DIRECTION DUE TO ANY INPUT FROM ME. AT NO TIME DID THE TWR CANCEL OUR TKOF CLRNC. AT NO TIME DID I BELIEVE THAT SAFETY WAS JEOPARDIZED. HOWEVER; COM WOULD HAVE LED TO BETTER UNDERSTANDING OF THE SIT. SUPPLEMENTAL INFO FROM ACN 377093: AS WE WERE ROLLING DOWN THE RWY; A COMMUTER ACFT (TYPE UNKNOWN) ENCROACHED ON OUR RWY. TWR TOLD THEM (IN EXCITED VOICE) TO STOP. THE ACFT CONTINUED TO CROSS AT TXWY J INTXN. AS FO; I WOULD NOW SAY I WOULD'VE INITIATED REJECT PROCS MYSELF; THE AGREED UPON (BY CAPT AND MYSELF) CONCLUSION WITH THE SAFEST RESULT. OUR CONTINUED TKOF WAS 'SAFE;' AS FAR AS THERE WAS ENOUGH CLRNC IN THIS SIT; THOUGH. MORE COM BTWN CAPT AND I WOULD'VE MADE THIS SIT EASIER TO HANDLE.