CL65 FLT CREW DESCENDS BELOW 1500 FEET PRIOR TO CRI DURING THE VOR RWY 13L APPROACH TO JFK WHILE LOOKING FOR TRAFFIC IN VMC.

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DURING VOR 13L APCH TO RWY 13L; JFK TWR ISSUED A LOW ALT ALERT WHILE THE ACFT WAS OVER CRI VOR. THE ALT WAS APPROX 1000 FT MSL AND DSNDING WHEN AN ALERT WAS ISSUED; TWR PROVIDED A CURRENT ALTIMETER READING; AND INSTRUCTIONS TO 'CORRECT IMMEDIATELY.' THE XING RESTR WAS 1500 FT MSL OVER THE CRI VOR PER INST APCH PROC (IAP) PUBLISHED BY THE FAA. CONDITIONS WERE VMC. THE CREW BECAME DISTR DURING AN ATTEMPT TO OBTAIN/MAINTAIN VISUAL CONTACT OF PROCEEDING LNDG TFC. WHILE BOTH CREW MEMBERS WERE 'HEADS UP' SCANNING FOR TFC; INCORRECT INPUTS WERE ENTERED INTO THE AUTOPLT CTLS. THE ACFT BEGAN AN EARLIER THAN PRESCRIBED DSCNT. AFTER THE POSTFLT DEBRIEF; THE FO AND MYSELF DETERMINED THE PROBABLE CAUSE TO HAVE OCCURRED AFTER THE FIRST PRESCRIBED DSCNT FROM THE ASALT FIX. DURING THE INITIAL DSCNT; THE FLT GUIDANCE COMPUTER CAPTURED THE 'PRESELECTED ALT;' COMPANY PROCS REQUIRE A VERBAL ANNOUNCEMENT OF 'ALTS CAP' BE MADE WHEN THE FMA FLASHES 'ALTS CAP.' DURING THE DSCNT FROM 3000 FT TO 1500 FT (ASALT-CRI) THE FGC CAPTURED THE PRESELECTED ALT OF 1500 FT; AT WHICH TIME 'ALTS CAP' WAS VERBALLY ANNOUNCED BY THE CREW MEMBERS; AND THE COMMAND TO 'SET NEXT ALT' WAS ISSUED FROM THE CAPT. THE FO (PNF) BEGAN TO SET THE NEXT ALT WHICH PER THE IAP WAS 800 FT. HOWEVER; DURING THE SELECTION OF NEXT ALT BY THE FO; I WAS SIMULTANEOUSLY ADJUSTING THE RATE OF VERT DSCNT ON THE FGC. THE SETTING I WAS ADJUSTING WAS THE 'VERT SPD;' HOWEVER AFTER THE FMA DISPLAYS 'ALTS CAP' NO INPUTS SHOULD BE MADE OR A DEFAULT FLT MODE OF 'PITCH' WILL BE COMMANDED ON. WITH 'PITCH' NOW ACTIVE ON THE FMA; AND A NEW LOWER ALT (800 FT) PROVIDED THE ALT CAPTURE AT 1500 FT NEVER OCCURRED; AND THE ACFT BEGAN A CONSTANT DSCNT TO 800 FT PRIOR TO REACHING THE CRI VOR; ALSO DESIGNATED AS THE FAF. WITH BOTH PLTS SCANNING OUTSIDE THE COCKPIT FOR TFC; THE ERROR WAS NOT NOTICED UNTIL THE TWR PROVIDED ALERT WAS ISSUED.