GTA, a semi-autonomous body which administers Darjeeling, Kalimpong and Kurseong sub-divisions, was formed in 2011.
Banerjee, who was speaking at the oath-taking ceremony of the newly-elected board members of the GTA, assured the people of Darjeeling that the state government would extend all support.
Gurung has been on hunger strike at the GJM's office in Singamari in Darjeeling since Wednesday.
He had last week urged West Bengal Chief Minister Mamata Banerjee to defer the polls until the Memorandum of Proposal (MoP) submitted by the GJM was implemented in the hills.
Gorkhaland long-term vision to be achieved non-violently; focus on good governance now: Ajoy Edwards
Ajoy Edwards claimed that the approach to achieve Gorkhaland has been a wrong one since the beginning, and called for a pan-India sympathy for the cause.
The GJM, at the meeting, dropped its long-standing demand for a separate state of Gorkhaland and instead sought a political solution within the state.
During the day, a GJM delegation, along with members of Hamro Party, held a meeting with Chief Minister Mamata Banerjee, who is on a scheduled five-day visit to North Bengal.
Rohit Sharma, an ex-legislator of the Gorkha Janmukti Morcha (GJM), also followed suit. Both of them were handed over TMC flags by state ministers Moloy Ghatak and Bratya Basu.
India saw a lot of resistance in 2017, the public went against the government to make things go their way.
The state had accused its northern neighbour of giving shelter to the GJM supremo who is wanted in several cases including Unlawful Activities (Prevention) Act) (UAPA), murder, rioting and arson.
Gurung has been evading arrest since August when cases were lodged against him under the stringent Unlawful Activities (Prevention) Act for his alleged involvement in several bomb blasts in Darjeeling
Tamang blamed party supremo Bimal Gurung for violence in the hills and said the people of the region "will not allow Darjeeling to turn into Kashmir".
The move, the CM Mamata Banerjee hoped, will be welcomed by the people of the Hills though a few may not like it personally.
Ousted Gorkha Janamukti Morcha leader Binay Tamang on Thursday asserted that the fight for Gorkhaland state would continue but appealed for withdrawal of the three-month-old shutdown.
The GJM representatives said the onus to initiate the talks on Gorkhaland lay with the Centre as Mamata has already declared that creation of a separate state is beyond her jurisdiction
Ousted leader Binay Tamang on Sunday challenged GJM chief Bimal Gurung to "come out of hiding" and lead the Gorkhaland movement from the front.
July, August and September are the peak months when most tourists visit the hill station. But since the strike and the total shutdown, the tourism sector has been completely affected.
The police had yesterday issued a lookout notice against the GJM chief for his alleged involvement in various cases, including a bomb blast in Kalimpong police station which killed one volunteer.
The chief minister held talks with political parties of Darjeeling hills and requested them to withdraw the indefinite bandh.
China could exploit the unrest between the Gorkhas and the Bengal government to fuel unrest in the Northeast.