However, Communist Party of India-Marxist party secretary Kodiyeri Balakrishnan has said the appointment has been approved by the state unit of the party.
In his letter to Yechury, Achuthanandan has said that Gopinath's policies do not match the economic policies of the party.
The appointment of Gopinath was confirmed earlier this week after the 38-year-old economist said that her position is just honorary and she is not moving to Kerala and will not be involved in economic policy decisions.
The top Congress party leadership here had earlier expressed "surprise" at the appointment of Gopinath.
Balakrishnan told the media on Thursday that the appointment of Gopinath was discussed at the state party level and the state secretariat had cleared it also.
"Just because she has been appointed the advisor does not mean that we will take all what she says. She will only give her advice," said Balakrishnan.
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