Not only were Nazi war criminals released relatively early into their sentences, but also Japanese war criminals. This largely took place in the mid-1950's, not only by the United States, but the majority of the Western Allies, who realised that there was limited political value in holding war criminals, who were seen as a relic of the immediate post-war disgust by the Allies of atrocities committed by the Axis forces.

While there continued to be a desire to punish those who had committed such atrocities, it was also countered by a perceived need to move on from the war, and engage in the Cold War.

Especially in regards to Japanese war criminals, it was felt that releasing them would strengthen ties to Japan, and limit the perception of a punitive occupation. While I don't have similar sources for Nazi war criminals, it seems likely that the Western Allies held similar conceptions in relation to West Germany, which was the centre point of the Cold War at the time.

Another aspect was that the Soviets still had a large number of German POWs at the time. By releasing war criminals early, the Western Allies were able to claim that they had legitimate claims to representing freedom and international cooperation. The influence of international religious and pacifist organisations also influenced diplomats and politicians, as well as the general public, with a growing campaign for clemency.

Sources:

Wilson S., Cribb R., Trefalt B., and Aszkielowicz D., "Japanese War Criminals and the Politics of Justice, 1945-1958" 2017.