TCASII RA DURING DEP FROM JFK.

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I WAS FO ON FLT XXX JFK TO LHR ON 12/AA/95. WE DEPARTED RWY 31L. AFTER CRI WE WERE TOLD TO TURN L HDG 070 DEGS AND CLB TO 11000 FT. PART WAY THROUGH THE CLBING L TURN; THE CAPT; WHO WAS FLYING; CALLED OUT CONFLICTING TFC ABOVE AND TO OUR L. HE ROLLED OUT OF THE TURN AND BEGAN TO LEVEL THE ACFT. SIMULTANEOUSLY THE ATC CTLR TOLD US TO TURN FURTHER L TO A 060 DEG HDG AND STOP THE CLB. AS THIS WAS HAPPENING WE RECEIVED A TCASII RA TO DSND. THE CAPT MAINTAINED VISUAL CONTACT WITH THE TFC AND MADE A SLIGHT DSNDING TURN TO THE R AT WHICH TIME I LOST SIGHT OF THE TFC. THE TCASII DISPLAY SHOWED THE TFC AT LESS THAN 1 MI AND 200 FT VERTLY. AS WE ACCELERATED CLR OF THE TFC I QUERIED THE CTLR AND HE GAVE US A L TURN AND RECLRED US TO 11000 FT. THE REMAINDER OF THE FLT WAS NORMAL. SUPPLEMENTAL INFO FROM ACN 324086: RECOGNIZING A POTENTIAL DANGER WITH THE OTHER ACFT AND WANTING TO AVOID A WAKE TURB ENCOUNTER; I ELECTED TO ROLL OUT OF THE TURN AND LEVEL OFF WHILE KEEPING THE OTHER ACFT (B747) IN SIGHT. LEVELOFF OCCURRED AT APPROX 500 FT BELOW THE B747 AND ABOUT A MI AWAY AT THE 3:30-4 O'CLOCK POS. THE B747 WAS DSNDING AT OR NEAR 8000 FT. NO INJURIES OCCURRED IN THIS CTLED MANEUVER.