These are two separate issues. The "war crimes" question is usually two or three separate questions:
Were the actions of the Allies considered war crimes at the time? (Or would they have been so, if the Axis had done them?)
If so, why weren't they charged with them?
Would they be considered such today?
Which has been addressed in other threads at great length (in short: 1. mostly "no," because of certain narrow ways in which the Allies construed the concept of war crimes and interpreted the relevant treaties; 2. because the Allies ran the tribunals and were not going to prosecute themselves, and were the ones who got to do that act of interpretation; 3. probably "yes," based on treaties joined after WWII, and changing norms about the targeting of civilians, but even then, international law is complicated and the status of nuclear weapons within them is pretty unclear).
This is separate from the issue of the UN calling for elimination — which the US was happy to join in on, providing that it was done in a way that could be verified (so you didn't have secret nuclear arms possession). The latter is what was known as international control of atomic energy and was discussed at length by the UN Atomic Energy Commission (not to be confused with the US agency known as the Atomic Energy Commission) from early 1946 through 1950 or so.
The intersection is not that pronounced: the calling for an elimination of nuclear weapons was not necessarily a repudiation of the actions of the US during WWII. It is rather an extrapolation of the technology into the postwar (and later Cold War): the US weapons were relatively small (compared to plans already on the books), hard to deliver, and very few in quantity (only a handful existed). But anyone could see that delivery would be improved over time (better bombers, later rockets), quantity was just a matter of time (they accumulate, even if you don't expand production, which they did), and the scientists were well aware that there were much larger weapons on the horizon (they were already thinking about multi-megaton fusion weapons). So they feared, correctly, that the future would be a much more dangerous place if the nations of the world accumulated atomic stockpiles in the same way they accumulated conventional (or even chemical) stockpiles.
So international control, which the US itself advocated for officially, was less about "the atomic bomb is a bad weapon inherently" and more about "if we have an atomic arms race, we will end up in a very ugly place, so let's use diplomacy to put a stop to that." Of course, they totally failed at this, for a lot of political reasons, but that's another story. (As I like to tell my students, we live in the maximally scary outcome that scientists of the 1940s could imagine.)
On the push for international control, Alice Kimball Smith's A Peril and a Hope: The Scientists; Movement in America: 1945-47, is a standard reference. Michael Gordin's Red Cloud at Dawn also has some very nice sections on the push for, and failure of, international control.