Banerjee also demanded that Planning Commission should be brought back.
In a letter to Modi on Thursday which was officially made public on Friday, Banerjee suggested the government focus on the Inter-State Council with "appropriate modifications" to "deepen cooperative federalism and strengthen federal unity".
Banerjee later told media that Planning Commission was more effective than NITI Aayog. "It would have been more successful. Planning Commission should be brought back," she said.
She alleged that NITI Aayog decides the agenda of the meetings unilaterally based on the BJP's interests.
"In NITI Ayog there is no scope for the states to articulate their stand. It decides three-four issues close to the BJP's heart. NITI Aayog decides the agenda," she said.
"There is no scope to discuss the state's annual plan, financial situation. Niti Ayog has no power, it is just a show-off," Banerjee said.
Banerjee also claimed in the three-page missive that the National Development Council, "which has been given a quiet burial", be subsumed within the broadened constitutional body, the Inter State Council.
"Given the fact that Niti Aayog has no financial powers and the power to support state plans, it is fruitless for me to attend the meeting of a body that is bereft of any financial powers," she said, intensifying her battle with the Centre.
Banerjee, in her letter, traced the history of the NITI Aayog ever since it was formed on January 1, 2015, to replace the Planning Commission.
Banerjee had on earlier occasions also stayed away from Niti Aayog deliberations to drive home her annoyance at the dissolution of Planning Commission.
The June 15 NITI Aayog governing council meeting, to be chaired by Modi, is slated to discuss multiple issues relating to water management, agriculture and security.
It is the fifth meeting of the governing council - the apex forum of NITI Aayog - that is consists of all Chief Ministers, Lieutenant Governors of Union Territories, several Union Ministers and senior government officials.
Banerjee has been on a collision course with the Modi-led Centre and scaled up her annoyance by skipping the oath-taking ceremony of the Prime Minister-led new Council of Ministers late last month.
( With inputs from IANS )