B777 FLT CREW WITH N90; EXPERIENCED NMAC/TCAS RA AT 6000 DURING VECTORS TO ILS 22L AT EWR.

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WE WERE RECEIVING VECTORS FOR AN ILS APCH TO RWY 22L AT EWR. LEVEL AT 6000 FT MSL; HVY ACFT TFC IN THE AREA AND ALSO ON THE RADIO FREQ. NOTICED AN ACFT CLBING QUICKLY THROUGH 5500 FT AT LESS THAN 1 MI AHEAD. RECEIVED TCAS TA ALERT; BUT WAS UNABLE TO BREAK IN ON RADIO FREQ. THEN RECEIVED RA ALERT AND ADVISED PF; I WAS IN THE R SEAT AND PLT MONITORING; TO RESPECT TCAS ALERT AND 'GO.' WE CLBED QUICKLY TO ABOUT 6800 FT AND FINALLY ADVISED APCH CTLR OF OUR ACTIONS AND THAT WE HAD RECEIVED A TCAS RA. CTLR SEEMED ALMOST UNINTERESTED AND ADVISED US TO LEVEL AT 6500 FT; ADDITIONALLY HE ADVISED OTHER TFC TO LEVEL AT 6000 FT AND TURN TO A HDG. THE CTLR THEN PROCEEDED TO CONTINUE TO ADVISE OTHER ACFT AND WHEN WE WERE ONCE AGAIN ABLE TO COMMUNICATE ON THE FREQ WE ADVISED THAT THIS WAS AN 'RA;' AND DID HE WANT US TO REMAIN AT 6500 FT? THE CTLR GAVE US A HDG AND A RETURN TO 6000 FT; NOTHING FURTHER WAS MENTIONED OF THE INCIDENT AND WE WERE VECTORED TO THE APCH AND HANDED OFF TO THE TWR CTLR. THE OTHER ACFT ULTIMATELY CAME TO WITHIN 200 FT OF OUR ALT AND WAS JUST UNDER OUR NOSE.