President Trump is expected to hold Mideast peace-focused conversations with both Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas during the UN General Assembly meeting in New York later this month, CBS News has learned.

The conversations will take place on the sidelines during Mr. Trump's first UNGA meeting since taking office. But diplomatic sources cautioned that it would be optimistic to think that the three leaders would be in the same room, CBS News White House and senior foreign affairs correspondent Margaret Brennan reports. The UNGA convenes on Sept. 12.

Brennan confirms that a meeting has been scheduled between Presidents Trump and Abbas during UNGA, according to a Palestinian diplomat.

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A White House official confirmed that two presidential advisers leading the peace initiative, Jared Kushner and Jason Greenblatt, would accompany the president to the annual gathering.

"The president will be meeting with a variety of world leaders at UNGA about a variety of different topics and we will share more details once the president's schedule is confirmed," the White House said in a statement. A White House official said that the "conversations about peace will be ongoing both before and after UNGA."

Kushner is spearheading the peace initiative, which remains in its infancy. He recently visited Israel, Palestine, and other influential Arab states in the region in what diplomats said appeared to be an attempt to survey the landscape and explore what might be possible. Jordan, Saudi Arabia, and Qatar were among the stops.

Greenblat, a presidential adviser on international negotiations, accompanied Kushner on the trip and has been leading the hands-on shuttle diplomacy involved in managing the complicated regional relationships. His efforts have been focused on projects like getting Israel to share additional water supplies with the Palestinian populations in the West Bank and besieged Gaza Strip.

"Everyone understands how complicated, difficult and challenging this task is, and that it will take time, but we are all feeling hopeful after all of our meetings last month," a White House official said.

"There is no peace process," said one diplomat from the region.

Israeli diplomats expect Mr. Trump to meet with Netanyahu around Sept. 18, according to the Israeli newspaper Haaretz.

CBS News' Margaret Brennan contributed to this report.