Beijing and Shanghai have given no indication of whether the bans will be lifted.
Other bike-rental companies are considering raising prices, as warmer weather brings a likely rebound in trip numbers.
Chinese bike-rental firms, Mobike and Hello Transtech, expressed their willingness to enter the bidding.
The law comes as concern mounts about the financial stability of a number of mobility firms in the rental economy sector.
Foshan will require Mobike, ofo, and other bike rental companies to hand over users blacklisted for bad parking.
Didi’s struggles in the bike-rental market led to a launch of its own brand, Qingju.
The rules went into effect on Wednesday on Didi’s bike-rental platforms Qingju and Bluegogo.
Cash-strapped Ofo could try wheeling its business down another path.