The CBI is following the orders of the BJP and has become the "BJP Bureau of Investigation" that has singled out opposition leaders, Kolkata Mayor and TMC leader Firhad Hakim alleged.
Both Houses of Parliament saw repeated disruptions amid protests by opposition parties over the Centre-West Bengal standoff.
Contesting the claims, senior advocate AM Singhvi said, the West Bengal Police and Kumar were fully cooperating with the agency.
Mamata Banerjee called off her dharna on Tuesday claiming moral victory after the Supreme Court directive.
Banerjee said she has "great respect" for the CBI and urged it to speed up its probe into theft of the Nobel medal of Rabindranath Tagore.
The UP CM also referred to the Supreme Court's order directing Kolkata Police Commissioner Rajeev Kumar to "faithfully" cooperate with the CBI in the investigation of the Saradha scam.
Rajeev Kumar was once a blue-eyed boy of former West Bengal chief minister Buddhadeb Bhattacharya.
Centre asks Mamata government to initiate disciplinary proceedings against Kolkata top cop Rajeev Kumar
The Union Home Ministry, which is the cadre controlling authority of the Indian Police Service officers in the country, has asked the West Bengal Chief Secretary to initiate the process.
Gowda's son and Karnataka CM HD Kumaraswamy too accused the Central government of damaging constitutional institutions by using them to target BJP's political opponents.