In a statement, Stalin urged the party members not to resort to activities that will lead to their death.
Karunanidhi's son expressed his condolences to the families of the dead DMK members.
Citing the statement of Kauvery Hospital where the 94-year old veteran politician is admitted, Stalin said their leader's health was normalizing.
On July 31, the hospital said Karunanidhi will have to be remain warded for an extended period owing to age related health issues including altered liver function.
Karunanidhi, who was Tamil Nadu's Chief Minister for five times and who has never lost an election in the 13 times he has contested, was admitted to the Kauvery Hospital on July 28 following a drop in blood pressure.
"He was resuscitated and stabilized in the ICU (intensive care unit) and managed by a team of doctors and nurses," the statement said.
"There was a setback on his clinical condition on July 29 due to difficulty in breathing. He responded well to medical management and his vital signs are gradually normalized," it said.
According to the hospital, Karunanidhi continues to maintain his vital signs with active medical support.