Here are the 10 latest developments:
Speaking to reporters this morning, Mr Kumaraswamy said: "I will request the director not to release the movie in the present situation. After the issue gets over then releasing the move will help him."
"Kaala" is facing the anger of pro-Kannada groups who have threatened to disrupt screenings if the movie releases despite a ban by a Karnataka film body.
Rajinikanth appealed to the Karnataka Chief Minister to facilitate the film's release by providing security at movie theatres in the state.
Rajinikanth, who is from Karnataka, said in Kannada: "I understand HD Kumaraswamy's situation. This is not good for Karnataka. When the film is released around the world, the Karnataka ban would highlight the issue (Cauvery water dispute)... The Film Chambers is supposed to ensure that there's no problem for distributors. It is not right that the Karnataka Film Chamber demands Kaala".
The appeal followed a Karnataka High Court order that asked the state government to provide security to theatres that want to screen Kaala in Tamil and other versions from Thursday.
Last month, after the Congress government of Siddaramaiah was voted out of power in Karnataka, Rajinikanth had reportedly said no matter which government takes over, Karnataka should release Cauvery waters for Tamil Nadu.
Mr Kumaraswamy urged Rajinikanth to visit the state and see the condition of farmers and the water level in the dams before commenting on the matter.
Rajinikanth, who announced his political debut in December 2017, has not made that visit yet but another actor-politician Kamal Haasan did. On Monday, Kamal Haasan met with Mr Kumaraswamy.
The 765-km long Cauvery river, also called the Ganga of the south, is the lifeline for both Karnataka and Tamil Nadu. The distribution of water between the southern neighbours has been disputed for over a century.
In a landmark ruling in February, the top court reduced Tamil Nadu's share of water while raising Karnataka's part. The court had also ordered a Cauvery Management Board to monitor the release of Cauvery water to Tamil Nadu by Karnataka. Karnataka has said it doesn't have enough water to release.
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