FLC OF A B737-300 STOPPED THEIR DSCNT IN RESPONSE TO A TCASII RA WHILE FOLLOWING A HDG AND ALT CHANGE GIVEN BY THE ARTCC CTLR. THE CTLR HAD GIVEN THEM THE CHANGE TO AVOID TFC; ONLY TO TURN THEM IN TO OPPOSITE DIRECTION TFC BY A CTLR TRAINEE.

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DURING LEVEL CRUISE AT FL350; APPROX 60 NM NE OF ZIZZI INTXN; WHILE OPERATING ON OUR ASSIGNED FILED ATC RTE (J174) HEADED S; ATC INSTRUCTED OUR FLT TO 'TURN L 10 DEGS; VECTORS FOR YOUR DSCNT; DSND TO FL310.' I READ BACK '10 DEGS L; DSND TO FL310.' ESTABLISHED ON THE NEW HDG (OFF THE AIRWAY) AND DSNDING THROUGH FL341; WE RECEIVED A TA ON TCASII ALERTING US OF AN ACFT AT OUR 11 O'CLOCK POS AND APPROX 1000 FT BELOW US WITHIN 5 MI OF OUR POS. THE PF (CAPT) SELECTED ALT HOLD ON THE MCP AND THE ACFT LEVELED OFF AT FL340 AFTER A BRIEF DSCNT TO APPROX FL338. I; THE PNF; ASKED ATC IF SHE HAD INTENDED FOR US TO MAKE THE TURN TO THE L AS WE WERE INSTRUCTED PREVIOUSLY; SINCE IT HAD PUT US IN CONFLICT WITH OPPOSITE DIRECTION TFC BELOW US. HER RESPONSE WAS AMBIGUOUS TO THIS QUESTION; BUT NO CORRECTIVE ACTION WAS REQUESTED BY ATC. A NEW CTLR TOOK OVER THE COMS AT THIS POINT. WE REQUESTED TO MAKE A R TURN BACK DIRECT TO ZIZZI; BUT WE WERE DISALLOWED THIS DUE TO TFC OFF OUR R. AFTER THE CONFLICTING TFC PASSED OFF OUR L; WE CONTINUED OUR DSCNT TO FL310.