Apart from NABL, what are the other national and international accrediting bodies for laboratory quality services?
International accreditation for Lab services (ILAC) is there but Indian government point of view, NABL is more than enough. You can try ISO, NABL.
College of American Pathologists (CAP) is one of accreditation for lab, link : https://www.cap.org/laboratory-improvement/accreditation/laboratory-accreditation-program
ILAC is the international organisation for accreditation bodies operating in accordance with ISO/IEC 17011 and involved in the accreditation of conformity assessment bodies including calibration laboratories, testing laboratories, medical testing laboratories