UNITED NATIONS — President Trump will try to play the peacemaker in his first appearance at the United Nations General Assembly this week, but not on the issue that American presidents have historically spent their energy and prestige on at diplomatic gatherings like this.

Rather than seek to revive the moribund peace negotiations between Israel and the Palestinians – as his predecessor, President Barack Obama, did at his first General Assembly – Mr. Trump is likely to wade back into the internecine feud between Qatar and its Persian Gulf neighbors.

Mr. Trump’s focus on the Gulf over the Levant attests to the chronically dismal conditions for an Israeli-Palestinian peace accord, but also to the diminishing role that the peace process plays in the geopolitics of the Middle East and to this president’s other priorities in the region.

“If they want to solve the problem, they’ve got to get a negotiation going” with the Israeli and Palestinians, said Martin S. Indyk, the special envoy for Mr. Obama’s last effort to broker a deal. “Unless Trump is prepared to bang some heads together there’s not much for him to do in this situation.”