He also appealed to the state to "take appropriate measures" to bring normalcy to the region.
"Our President has sent a letter to Chief Minister and appealed that state government must take appropriate measures to address all the issues including the present crisis on a permanent basis and ensure that normalcy returns to Darjeeling," GJM's leader Swaraj Thapa said.
The Darjeeling hills have been on the boil for over two months with an indefinite shutdown called by the GJM continuing since June 12 to press for a separate state of Gorkhaland.
He, however, said Mr Gurung reminded that the GTA (Gorkhaland Territorial Administration) was only to be an interim arrangement as per the tripartite MoU and the party has not dropped its demand for Gorkhaland.
"...we request your honour to initiate political dialogue on the long pending demand of the Gorkhas, which is Gorkhaland to help to resolve the present crisis of Darjeeling," Mr Gurung said in the letter.
However, Ms Banerjee had on Tuesday announced the state government would hold talks with "all major political parties" on August 29 in a bid to restore peace and normalcy in the agitation-hit north West Bengal hills.
Mr Gurung also demanded a Central Bureau of Investigation or judicial inquiry into deaths caused due to police action, withdrawal of all the cases against agitators and that those detained during the agitation be released.
He also demanded compensation for the kin of those who have been "killed in police firing" and the injured.
Mr Gurung said the creation of autonomous bodies in Darjeeling, first as the Darjeeling Gorkha Hill Council in 1988 and then as the GTA in 2011, has "failed miserably" and "never fulfilled the people's aspiration under the Statesman of West Bengal".
"The two failed councils in the Darjeeling hills today should pave ways for us to learn from our previous mistakes that experimental models to temporarily curb people's aspiration for separation from West Bengal has not worked in the past, nor the present," he said.