BJP condemned the act while Sinha said he was ready for a debate with those who had put up the posters.
"BJP condemns these posters. This is the job of some mischief makers and we condemn the act," party spokesperson Shahnawaz Hussain said.
Sinha said, "I wish those who are responsible for putting up these defamatory posters identified themselves so that we could start a debate."
The former union minister had issued a statement to PTI on November 20 in which he had demanded that Gadkari should immediately step down from the post of president. He had insisted that whether the charges against Gadkari have been proved or not, those in public life should be above reproach.
Sinha had also said Gadkari's continuance in office would dent the BJP's fight against corruption in the Congress-led UPA government.
BJP Rajya Sabha member Ram Jethmalani was the first one to openly demand Gadkari's resignation. Party national executive member Jagdish Shettigar too stated later that Gadkari should step down.
There are charges that Gadkari's Purti Group has been funded in a dubious manner. RSS ideologue and CA S Gurumurthy had, however, given Gadkari a clean chit.