You may be interested in an earlier post of mine that covers the papacy during WWII

I cannot speak to the pope's position during the Rwandan genocide.

Statements from the papacy are a bit unique. As José M. Sanchez explains in The Spanish Civil War as a Religious Tragedy:

whatever the pretensions of papal power, the fact is that the pope is a human being, the Vatican is a state, the Holy See is a diplomatic institution, and all of them are subject to the limitations inherent in their condition

Not only are they comments from the leader of one of the world's largest religions, but they serve other purposes as well. For the past few hundred years, the papacy has been loathe to invite any split in the Church, what we call a schism. The pontiff is also a head of state, albeit a tiny one. As such, he has access to diplomatic channels and initiatives, but is also limited by treaties and other obligations. However, the pope has no military force with which to enforce his desires outside of the Vatican, so the more direct means of getting his way are unavailable. Also, the pontiff is human, and can only act on things he is aware of. Further, he must discern truth from propaganda--not always a trivial task.

Intervention is a difficult subject. Under the Just War theory, a number of factors need to be met before the use of force is considered legitimate. Skipping some of the legal hurdles, one of the larger questions would be the probability of success. That force should be a last resort is also a concern. The biggest issue would likely be the idea of proportionality, meaning that the actions to be prevented be more destructive than the likely destruction caused by the use of force. Given the history of institutional deference to Just War theory, the pope is historically unlikely to advocate the use of force in most situations.

The papacy has consistently opposed violence against noncombatants, including aerial bombardment (including nuclear weapons), indiscriminate use of force (including poison gas and biological weapons), the destruction of culturally significant objects, and genocide. I am most familiar with WWII and the Spanish Civil War, but followup questions are always encouraged.