Danforth has two main reasons as to why he won't pardon any prisoners. The first reason is that, at this point in Act Four, some of the accused have been hanged. He tells Parris and Hale that to pardon people at this point would not be fair to those who have been hanged.
You misunderstand, sir; I cannot pardon these when twelve are already hanged for the same crime. It is not just.
Danforth also thinks that to change his mind at this point will challenge his credibility and the reputation of the court. Even as Parris warns him that this witch hunt might incite a rebellion, Danforth sticks to his word and will not reconsider his judgment. Danforth is concerned primarily with his and the court's reputation. He justifies sticking to his judgment by conflating his judgment with God's law. He has convinced himself that he (like God) can not be wrong:
While I speak God's law, I will not crack its voice with whimpering. If retaliation is your fear, know this - I should hang ten thousand that dared to rise against the law, and an ocean of salt tears could not melt the resolution of the statues.
The fact that Danforth's credibility might suffer is an important one. But it goes beyond his status as an official of the court. This man, whose intelligence and charisma have allowed him to be appointed to a powerful position, is also clearly an arrogant man. His flair for the dramatic lends a performative quality to his words which goes beyond the dramatic power present in Miller's writing. It is important for Danforth to be portrayed as a force of authority but also as a figure whose voice and manner are compelling and persuasive.
Clearly Danforth sees any kind of wavering on the sentences of the accused to show weakness or lack of authority on his part; not to mention having to admit he made a mistake. Therefore he states very strongly to the Reverends Parris and Hale that no pardons or postponements will occur, even though the village is in an uproar about the execution of the innocent:
"Now hear me, and beguile yourselves no more. I will not receive a single plea for pardon or postponement. Them that will not confess will hang. Twelve are already executed; the names of these seven are given out, and the village expects to see them die at dawn. Postponement, now, speaks a… a floundering on my part; reprieve or pardon must cast doubt upon the guilt of them that died till now."
Later, when Hale presses the point, he invokes God to say he will not postpone the executions:
"Mister Hale, as God have not empowered me like Joshua to stop this sun from rising, so I cannot withhold from them the perfection of their punishment."
And so here it must be pointed out that Danforth is a religious man and refers to his religious beliefs when deciding what to do. This was prior to the Bill of Rights, wherein our first amendment to the Constitution establishes a separation of church and state. Danforth seeks to align himself with these men of God, and tells Reverend Parris he will pray to God for guidance:
"Now, sir—which of these in your opinion may be brought to God? I will myself strive with him till dawn."
Danforth attempts to set himself on the same level of religious piety and authority as Parris and Hale, although he is himself not employed by the church.