The United States can take a role as mediator if a few conditions are met:
The first one is that the process of mediation needs to be within the confines of it’s own laws, foregoing 21st century political thought of the US federal government existing to “make the world a better place.” Mediation should happen within the confines of it’s Constitutionally delegated powers and founding philosophies.
Secondly, the US’ mediation needs to come with a revised outlook on the situation, abandoning the delusional thought process that because all humans are created equal, then they are striving after identical values, purposes, and goals. Acknowledging that people in the Middle East are indeed different than us has traditionally been seen as cynical at best and xenophobic at worse-but until the US comes to term with this and accepts the hard truths-they will remain ineffective in their middle eastern foreign policy. Earlier successes in Japan and South Korea made the US feel like their approach would be a one size fits all-and that has proven untrue, and indeed the international community at large-not just the US-has let this vision of “we are all the same” delude them and their approach to the Middle East and every associated issue that flows from it that is currently affecting the globe. In turn, the denizens of the Middle East appear, not so incorrectly, to view the attempt as modern colonialism, regardless of how much DC or Brussels may assure them “this time it’s different because this time we are really, really moral.”
mediation in the Middle East can more effectively resonate when the conflicting parties can sincerely trust that the US and west at large is operating on the actual principles it was built upon:self-determination and autonomy, rather than the retrofitted 21st century corruptions of them. A vested desire to see the nations of the region take the baton of sovereignty for themselves rather than a desire to bring them “into the global order.” It is only in this place of trust-an independent 3rd party nation standing alone and not as part of a global body seeking to enact sweeping global change-that the US can garner more trust for this kind of work.
We can perhaps infer Biblically that this peace may never happen, but if we aim for a solution, then maximize your chances of reaching it.