As many as 144 COVID related deaths were reported in the last 24 hours, taking the death toll to 14,612, the Health department said.
The state for the first time saw the daily cases cross 10,000 on April 18 and the 20,000 mark on May 2.
The new infections breached the 21,000 mark on Tuesday.
DMK president M K Stalin who is set to be the new chief minister took stock of the situation for the second consecutive day with Chief Secretary Rajeev Ranjan and senior government officials at his residence here.
In a statement issued later, Stalin urged people to follow the new restrictions that were announced by the government on Monday and said people should realise that the the second wave of the COVID-19 outbreak was much worse than the impact caused by the pandemic last year.
Appealing to the people to be very cautious he said, considering the high number of infections in Tamil Nadu and to break the virus chain new restrictions were announced by the government.
''Instead of thinking it as a government announced restrictions people should follow it as their own (restrictions) in order to be safe,'' he added.
''If it is the government responsibility to take care of the COVID-19 patients, it is the responsibility of the people to coordinate with the government in containing the virus spread,'' he said.
Meanwhile, recoveries on Tuesday aggregated to 11,09,450 with 19,112 patients being discharged, leaving 1,25,230 active infections, the bulletin said.
The State capital continued to constitute the bulk of the total cases accounting for 6,228 new infections, taking the overall tally to 3,58,573 till date.
The metropolis also leads in the number of fatalities with 4,894 people succumbing to the virus so far.
The number of samples tested in the last 24 hours stood at 1,40,512 pushing the cumulative number of specimens examined so far to 2,32,38,475.
Besides Chennai, Chengalpet added 1,608 cases, Coimbatore 1,509 and Thiruvallur 1,152, while 29 districts clocked new infections in triple digits indicating a sharp increase of the virus spread.
Among the 144 deceased, 34 including a 25-year old woman from Madurai succumbed to the virus without any pre- existing illness.
As many as 34 of them who tested positive in the last 24 hours were returnees from various destinations, the bulletin said.