The collegium met Wednesday but deferred its decision on reconsidering the name of Uttarakhand High Court Chief Justice KM Joseph for elevation to the Supreme Court.
Justice Joseph's name had been recommended by the collegium in January. It was recently returned by the government for reconsideration.
The government says Kerala, from where Justice Joseph hails, is already well-represented in the higher judiciary.
The government has also pointed to Joseph's lack of seniority. There are 44 high court judges more senior than him.
Commentators however have pointed out that Joseph had headed the Uttarakhand high court bench that had in 2016 overturned the Modi government's decision to impose President's rule in Uttarakhand, allowing the state's Congress government to return to power.
All five judges of the collegium — Chief Justice of India Dipak Misra, and Justices J Chelameswar, Ranjan Gogoi, Madan B Lokur and Kurian Joseph — were at Wednesday's meeting.
The justices reportedly discussed threadbare Law Minister Ravi Shankar Prasad's letter saying the government would like the collegium to reconsider its recommendation of Justice Joseph.
Most commentators have said the collegium will in all likelihood send its recommendation of Justice Joseph's name for promotion to the Supreme Court back to the government. And in which case, the government will have no choice but to accept the recommendation.
CJI Dipak Misra however had last week said the government was well within its rights to send back Justice Joseph's name for reconsideration.
On Wednesday, news reports quoted Law Minister Prasad as rejecting suggestions that the government was obstructing Justice Joseph's appointment as an SC judge because he had overturned the imposition of President's rule in Uttarakhand.
"It has nothing to do with that at all," the reports quoted Prasad as saying.
He also accused the Congress of levelling "sponsored allegations" against the NDA government.