CONFLICT BTWN 2 ACR ACFT.

Narrative

AFTER TKOF FROM JFK WE CHANGED TO AND CHKED IN ON 124.75 MH AND WERE CLRED 'DIRECT TO RBV-CLB TO AND MAINTAIN 17000 FT.' WE ACKNOWLEDGED. AS WE CLBED THROUGH ABOUT 14000 FT WE RECEIVED A TCASII TA OF TFC AT 1200 AND 2300 FT ABOVE US. I TOLD FO TO LEVEL AND TURN TO R. HE DID. WHEN I COULD GET A WORD IN WITH VERY BUSY ATC; REGARDING TFC; HE ADVISED; IN AN ANNOYED TONE; 'BEEN TRYING TO GET YOU ABOUT TFC.' ALL 3 CREW WERE PAYING ATTN AND NEVER HEARD ANY CALLS. SOMEWHERE IN ALL THE CONFUSION I HEARD '15000 FT' BUT NEVER HAD TIME TO CONFIRM IF IT WAS FOR US OR NOT. WE WERE INSTRUCTED TO CHANGE TO NEXT SECTOR AND I CHKED IN 'LEVEL AT 15000 FT CLBING TO 17000 FT.' SHE REPLIED 'CONFIRM CLBING TO MAINTAIN 17000 FT.' I DID NOT PURSUE ANY OF THE ABOVE BECAUSE ATC WAS VERY BUSY. WE HAVE NO IDEA HOW CONFLICT AROSE. ATC ERROR IN ASSIGNING 17000 FT. WE MISSED A CALL. CALL BLOCKED -- VFR ACFT -- ETC. WE SIGHTED OTHER ACFT TWIN TURBOPROP (SAAB?) AS HE PASSED OVERHEAD AT 1400 FT TCASII AND SLIGHTLY L OF OUR POS. IF IT HAD NOT BEEN FOR THE TCASII THIS COULD HAVE BEEN A DISASTER.