The South made such an offer but the North was slow in taking them up on it, resulting in additional POW deaths. From Judge Robert Ould, Confederate Agent of Exchange (Source: Point Lookout Prison Camp for Confederates, by Edwin W. Beitzell, copyright 1983):
When it was ascertained that exchanges could not be made either on the basis of the cartel or officer for officer and man for man, I was instructed by the Confederate authorities to offer to the United States Government their sick and wounded, without requiring any equivalents. Accordingly, in the summer of 1864, I did offer to deliver from ten to fifteen thousand of the sick and wounded at the mouth of the Savannah River without requiring any equivalents, assuring at the same time the agent of the United States, General Mulford, that if the number for which he might send transportation could not readily be made up from sick and wounded, I would supply the difference with well men. Although this offer was made in the summer of 1864, transportation was not sent to the Savannah River until about the middle or last of November, and then I delivered as many prisoners as could be transported, - some thirteen thousand in number, amongst, whom were more than five thousand well men.
Disagreements make no difference. Starving thousands of soldiers that are POWs is murder. The south was using them as hostages to make demands and allowed them to die when those demands were not met. That's terrorism.