"The first batch of the MBBS students would be completing at the end of this year without recognition for their degree," NECCC chairman D D Lapang said in a letter to Azad.
There is "simmering discontentment" among the students of the North-East in this regard, he said.
NEIGRIHMS has been functioning since 2002, but various problems, including shortage of faculty, has paralysed the institute.
Over Rs 550 crores has been spent so far in setting up the institute, whose first batch for the MBBS course was inducted in 2009, he said.
As per Medical Council of India (MCI) guidelines, NEIGRIHMS ought to have at least 140 teachers in the different departments for its MBBS course, but there are only about 45 at present, much below the required faculty strength.
Last year, MBBS students of the institution had resorted to a week-long strike to protest against lack of faculty members in the institute and also demanded official recognition to their course.
Congress president and UPA chairperson Sonia Gandhi had assured of necessary intervention to resolve the issues at the institute, Lapang said.
NECCC has also sought the Ministry's help in enabling NEIGRIHMS to be passed by an Act of Parliament, in line with AIIMS, to save it from further crises.
