Mr Gurung's counsel claimed before a bench of Justices A K Sikri and Ashok Bhushan that the state was proceeding in a "biased manner" against GJM members and there was an environment of "constant fear" in Darjeeling due to this.
Senior advocate P S Patwalia, representing Mr Gurung, sought an investigation by an independent agency in the cases lodged against the party members as also in their alleged extra-judicial killings by the police, maintaining that a fair probe was not expected from the state.
"We cannot expect a fair investigation. It is persecution. So probe by an independent agency is required," he said.
However, senior counsel A M Singhvi, appearing for West Bengal Police, said there were dangerous consequences of what the GJM leader was arguing before the apex court as there was a situation of public disorder.
During the hearing, Mr Patwalia raised the issue of alleged violation of human rights and extra-judicial killings by the state police and referred to a number of such purported cases.
He claimed that a GJM supporter was shot dead by West Bengal Police in Sikkim and a case has been lodged against the police officials there.
"GJM leaders are arrested in false cases," he said, adding "they are trying to effectively end the movement".
"There is an environment of constant fear in the Darjeeling region as the police is looking for GJM members. State is proceeding in a biased manner," he claimed.
The arguments remained inconclusive and would continue on December 8.
Mr Gurung had earlier told the apex court that main flash-point of confrontation was that the GJM had opposed the state government's move to make Bengali language mandatory in the schools in West Bengal.
The state police had maintained that Mr Gurung was absconding, not cooperating in the probe of cases lodged against him and playing "blatant politics", claiming that Mr Gurung was facing trial in 23 cases and several other criminal cases were lodged against him.
It had alleged that several serious incidents had taken place under Mr Gurung's leadership, including the killing of a 26-year-old police official during the recent Gorkhaland agitation.
The police has sought vacation of the court's November 20 order restraining it from taking any coercive step against Mr Gurung, who is seeking a probe by NIA or CBI in the killings of several Gorkhaland activists during the recent agitation.
The GJM central committee had recently suspended Mr Gurung for six months and appointed Binay Tamang as the party's new president.