At this point, even Danforth understands that the whole witchcraft hysteria was probably a hoax, and that he and the Puritan court had sent innocent people to their deaths. By Act IV he is trying to save face by urging them to confess so he can let them off the hook. But Proctor and the others aren't interested in lying to save the church's credibility or pride. This is frustrating to Danforth, and he feels like he has to follow through on the hangings then, or he would be essentially confessing his awareness of the hoax. He is truly in a no win situation by this point.
In Act IV, Reverend Hale tells Deputy Governor Danforth that he must pardon the prisoners because they refuse to admit to witchcraft. Danforth replies that he cannot pardon the prisoners because twelve people have already been hanged for the same charge and it would not be just. Danforth explains that the villagers expect to see the prisoners hanged tomorrow and if he postpones or cancels their executions, he will cast doubt on the court. Deputy Governor Danforth refuses to admit that the court is not infallible and that he may be wrong. Danforth fears that the people will revolt and his reputation will be ruined if he pardons the prisoners. Instead of doing the right thing and listening to Reverend Hale's advice, Danforth remains stubborn and selfish by refusing to pardon the prisoners.
Danforth is not trying to convince the condemned people to confess using witchcraft so he can "let them off the hook", he is specifically wanting John Proctor to confess because the true meaning of John's arrest and hanging is because he committed contempt of court and undermined/questioned Danforth's authority. This entire Salem witch trial is a game for Danforth, who is trying to assert and impress his theocratic power of the people. Danforth knew all along that Abigail and the other girls were pretending but the arrests and hangings he sentenced for the population was to prove his authority. The people who confessed to witchcraft, in his eyes, bought into and respected his power and the people who refused to confess are still fighting it.