The state government said it had so far held five rounds of talks with the unions on a range of issues, including pending post-retirement benefits, and added that there is "nothing more that it can do".
"It is in their hands. The employees will for sure take a good decision. The strike will fail. Chief Minister E Palaniswami has assured the workers of implementing their demands," Transport minister M R Vijayabaskar told reporters.
Seeking to reassure the public, the government said there was no need for concern as buses would be back on the roads soon.
With ten transport unions affiliated to various political parties, including DMK and left-wing outfits, participating in the strike, many buses across the state remained off roads.
Officials came up with alternative plans to clear the rush with private buses pressed into service in Chennai and other parts of the state.
Temporary drivers were also being deployed to ferry passengers, officials said.
In Chennai, people were still seen using alternative modes of transport such as the suburban train service, Metro rail, autorickshaws, share autos and taxis. Some commuters complained of overcharging by autorickshaws and share autos.
The Southern Railway is also operating extra services connecting Chennai and many other cities of the state, besides increasing the number of trips on the suburban routes in Chennai.
The transport unions had earlier said they would go on strike from Monday if talks held last week on various issues failed. However, a section of employees embarked on the protest from Sunday afternoon itself.