Kushner, Greenblatt, Haley, and Guterres also discussed recent votes taking place in the UN—the General Assembly voted Wednesday in favor of condemning Israel for "excessive use of force" against Palestinian civilians in Gaza and voted down a US proposed resolution condemning Hamas over the recent escalation of violence in Gaza.
Nabil Abu Rudeineh, a spokesman for Palestinian President Mahmoud Abbas, attacked the US plan, calling it "meaningless" and arguing it "will achieve nothing."
"Without the agreement of the Palestinian people, the fate of this round of meetings will be complete failure," he added.
A month ago, five of Trump's administration officials and a Congress parliamentary aide said that the White House intends to release its new Mideast peace plan shortly after the month of Ramadan.
However, the officials noted that the release of the plan could be postponed depending on developments in the region.
Meanwhile, Greenblatt and Kushner have been briefing US allies about the peace plan's details.
Another possible obstacle taken into account in promoting Trump's peace plan is the fact that the Palestinians might not even agree to review the plan, judging by recent developments.
Abbas recalled his envoy to the US Husam Zomlot back to Ramallah for consultations last month in protest of the US Embassy relocation to Jerusalem.
Abbas recently reiterated that, "The United States is no longer an honest mediator in the peace process, we will not accept any plan put forward by the United States because of this partisan spirit."
As part of the US's decision to change tactics at the UN, Ambassador Haley had proposed an amendment condemning Hamas for firing rockets at Israel and inciting violence along the Gaza-Israel border fence, "thereby putting civilians at risk."
In an unprecedented and dramatic move, the UN General Assembly voted last week in favor of condemning Hamas over the recent escalation of violence in Gaza, making it the first time in the UN's history in which a resolution against Hamas gains a majority.
The US amendment was approved by a 62-58 vote, with 42 abstentions. But General Assembly President Miroslav Lajcak declared that under an assembly rule, a two-thirds majority was needed, so the amendment failed.
In the following vote, the resolution to condemn Israel and call for an international force for the protection of Gaza's civilians was approved by a 120-8 majority, with 45 abstentions.
Diplomatic sources said it was not a question of if but of when the United States retreats from the Human Rights Council, which is holding a three-week session through July 6.
A US source, speaking on condition of anonymity, told Reuters the withdrawal appeared to be “imminent” but had no details.
A separate US official in Geneva had no information about a looming pull-out during the upcoming talks, saying: “We are still moving ahead with our engagement for the coming session.”
Haley publicly told the Council a year ago that Washington might leave the body unless a “chronic anti-Israel bias” were removed.
The US argues that since the forum was set up in 2006, it has been holding a permanent standing agenda item on what its members says are suspected violations committed by Israel in Palestinian territories, which Washington wants removed.