Buses, trams and underground trains are expected to remain in depots across many municipal transport companies due to the industrial action.
Mr Dingyadi urged the association to embrace dialogue while the government continues to work on addressing their concerns.
Residents and businesses are lamenting the days-long power outage in Osun.
The TUC President Festus Osifo said a communiqué on the strike suspension would soon be issued.
No worker would be victimized as a result of the industrial action.
“If you want to participate in the electoral process, wait until 2027. If not, then make peace. You are not the only voice of Nigerians,” Mr Tinubu said.
The National Executive Council meeting of the labour unions held on Monday in Abuja resolved to embark on strike.
“If the government fails to address these demands at the end of the three months, we will go ahead with our next line of action.”
Although Mr Falana did not categorically name anyone, several politicians have been meeting with Mr Tinubu at the Aso Villa since he emerged as president.
The federal government had earlier obtained a court order restraining Labour from embarking on a nationwide industrial action on Wednesday.
