Coun Douglas Johnson said franchising would mean decisions were made more in the public interest. He was responding to sharp criticism of transport operators by the mayor of Sheffield City Region.
Mr Jarvis hit out at a plan by transport operators, including First and Stagecoach, to increase bus and tram fares across South Yorkshire by five per cent from June 7.
The rise, just as people were returning to public transport - and after companies had been propped up with millions from the taxpayer - was ‘unacceptable’ he said.
Operators say it will pay for operating costs which have continued to increase during the pandemic.
Coun Johnson said the increase was ‘well above inflation’ and came after ‘regular bus fare increases’.
But he said the best way to prevent unjustified rises was by having public services in public hands. And Mr Jarvis had ‘not taken any meaningful steps’ on franchising, which would give him that control.
He added: “I don’t underestimate what a big job that is going to be, it’s a complex contractual job for the state to intervene and take control of the network.
“Transport companies have had big bailouts but they are private profit-making entities. Their takings are down and will be down for some time and they think price rises are in their commercial interests.”
The Greens also want franchising to create better and more reliable transport as a response to the climate crisis, he added. New price rises risked pushing people back towards cars.
Last year, a bus review said creating a municipal bus company owned and run by the Sheffield City Region should come no more than five years after the creation of a new South Yorkshire-wide Enhanced Partnership.
Mr Jarvis has said there will be an update on how buses are run in South Yorkshire at a meeting on June 7.
It has taken Greater Manchester more than four years to get to a position of bringing buses back into a form of public control.