AN MLG RESPONDED TO A TCASII RA JUST AS ATC WAS GIVING HIM A TURN TO MISS TFC.

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CAPT WAS FLYING; FO WAS TALKING TO ATC. FO CALLED CVG DEP AND SAID 'CVG DEP; ACR FLT IS OUT OF 2700 FOR 6000.' CVG DEP RESPONDED WITH 'ACR FLT RADAR CONTACT; CLB AND MAINTAIN 7000'. I ACKNOWLEDGED 7000 TO THE FO AS HE SET 7000 IN THE ALT ALERT. THE FO REPLIED TO CVG DEP 'ACR FLT CLB AND MAINTAIN 7000.' AT 5900 FT WE GOT A TA ON THE TCASII. IT SHOWED AN ACFT 12 O'CLOCK AND 10 MI; 1100 FT ABOVE US. FO CALLED OUT LEAVING 6000 FOR 7000. AT 6500; TA BECAME A RA AND SAID 'MONITOR VERT SPD.' AT THE SAME TIME; ATC ISSUED AN IMMEDIATE R TURN TO 270 DEG (APPROX A 70 DEG TURN). WE SAW THE CONFLICTING ACFT ON THE TCASII AT 5 MI AHEAD AND 500 ABOVE US. AT THE SAME TIME; WE ACQUIRED THE ACFT VISUALLY. I HAD STOPPED CLBING AND ACTUALLY DSNDED TO ABOUT 6300 FT IN THE TURN TO INCREASE SEPARATION. ATC CLRED US TO 12000 FT SAID 'THANKS FOR YOUR HELP.' CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: THE RPTING CAPT STATED THAT THE INTRUDER ACFT; AN LTT; WAS A 'POP-UP' ACFT ON HIS TCASII. HE ALSO STATED THAT; FROM THE DEMEANOR OF THE CTLR; THE CTLR HAD PROBABLY MADE AN ERROR AND HAD NOT SEEN THE TFC BEFORE THE RPTR MENTIONED THE INTRUDER. THE 7000 FT ALT ASSIGNMENT WAS HIGHLY UNUSUAL ON DEP.