GND INCIDENT; POTENTIAL CONFLICT. ABORTED TKOF TAKES MDT ACFT INTO A RWY INCURSION.

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WE WERE CLRED FOR TKOF ON RWY 3 AND UNBEKNOWNST TO US; AN ACR 727 WAS CLRED BY GND TO CROSS RWY 3 AT TXWY A. AS WE WERE ROLLING WE HEARD THE 727 SAY ON TWR FREQ THAT HE WAS CLRED TO CROSS. THE TWR THEN CALLED US A DIFFERENT CALL NAME AND SAID OUR TKOF CLRNC WAS CANCELED. BY THIS TIME WE WERE WELL PAST THE 727 AND COMING UP ON RWY 36. THE TWR TOLD US TO TURN L IMMEDIATELY WHERE THERE WAS NO TXWY; THEN HE TOLD US TO STOP. THE TWR WAS NOT CLR ON WHAT THEY WANTED NOR WERE THEY FAMILIAR WITH THE ARPT. SUPPLEMENTAL INFO FROM ACN 273770: I WAS THE FO ON A SCHEDULED 121 FLT FROM DCA TO ISP. CLRNC WAS GIVEN BY GND CTL TO TAXI TO RWY 3 FOR DEP. (RWYS 3; 33; AND 36 WERE ALL IN USE.) AT THE END OF THE TAXI; WE SWITCHED TO TWR FREQ AND AWAITED TKOF CLRNC. WE THEN RECEIVED AND ACKNOWLEDGED TKOF CLRNC FROM RWY 3. SINCE I WAS THE PF; I BROUGHT PWR UP TOWARDS 'TKOF PWR' AND STARTED THE TKOF ROLL. AFTER ROLLING APPROX 50-100 FT; A FLT XMITTED OVER TWR FREQ THAT HE WAS CLRED TO CROSS RWY 3. THE TWR CTLR CANCELED OUR TKOF CLRNC JUST AS I NOTICED A 727 XING THE HOLD LINE ON TXWY C. I ABORTED THE TKOF AND TAXIED CLR OF THE RWY AND RWY 36 WHERE ANOTHER PAX JET WAS ON SHORT FINAL. WE NEVER HEARD THE 727 RECEIVE HIS TAXI CLRNC BECAUSE WE WERE MONITORING THE TWR FREQ. IT'S COMMON PRACTICE FOR GND CTL TO CLR AN ACFT ACROSS AN ACTIVE RWY AND THEN INSTRUCT THAT ACFT TO MONITOR TWR FREQ ON THE OTHER SIDE. IF THE JET HADN'T SWITCHED OVER WHEN HE DID; WE WOULDN'T HAVE KNOWN THAT HE WAS ATTEMPTING TO CROSS. IN LOOKING BACK IT PROBABLY WOULD HAVE BEEN JUST AS SAFE TO CONTINUE THE TKOF. DCA IS A HIGH DENSITY ARPT AND THERE IS VERY LITTLE ROOM FOR ERROR; EITHER ON THE GND OR IN THE AIR. AN ADDITIONAL FEW SECONDS COULD MEAN THE DIFFERENCE IN FUTURE INCIDENTS.