Kushner addressed the Palestinian public via a local newspaper, Al Quds, urging them not to continue being led down a path of violence and conflict they their "scared" leadership.
Palestinian officials, who want East Jerusalem as the capital of a future state, accused Mr Kushner of trying to undermine Mr Abbas and what they described as their leader's moderate camp.
King Abdullah II, who met with Kushner and Greenblatt on Tuesday in the capital, Amman, will visit Trump at the White House on Monday to weigh in personally with the president.
Palestinian officials denounced U.S. envoy Jared Kushner on Sunday over remarks he made during an interview with a Palestinian newspaper, and accused him of "incitement" against Palestinian Authority President Mahmoud Abbas.
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Abbas has refused to see Trump's team since the embassy decision, accusing Washington of pro-Israel bias.
Kushner said that the proposal is still in the works, only promising that it will be ready "soon".
Kushner and Greenblatt's trip to Jerusalem followed a regional tour that included Jordan and Egypt - Israel's neighbors and peace partners - and Qatar, a Gulf state that has helped fund humanitarian aid to Gaza.
"The interview is part of the American administration's attempt to address the Palestinian people directly before presenting its peace plan", a US official told Israel's Channel 10.
"I must say that there was total support for our positions and actions to ensure the security of the State of Israel", Netanyahu said. Kushner says the plan is "almost done, " but offered scant details aside from the promise of economic prosperity.
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That coincides with the language of the worldwide consensus and global law, which hold that East Jerusalem and the West Bank are Israeli-occupied territory. Palestinians seek east Jerusalem as the capital of a future state.
Peace talks between Israel and the Palestinians have been stalled since 2014.
On Tuesday, Israel's air force struck several Hamas' military targets after terrorists deployed incendiary kites and balloons that caused severe fires in Israeli communities on the Gaza border.
The Health Ministry in Gaza Saturday unveiled a detailed official statistics on Palestinians killed and wounded by Israeli soldiers' gunfire since the outbreak of rallies and protests in Gaza Strip on March 30.
On Sunday, the IDF revealed evidence demonstrating that the Hamas terror group organizes and carries out kite-based arson attacks originating in the Gaza Strip, refuting claims that the terror activity represents the spontaneous demonstrations of young Gazans.
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It also said the army ordered 21 Palestinian families to leave their homes in the Jordan Valley so that soldiers can play their war games in the vicinity of their homes, as well as settlers torching West Bank fields near Nablus in the north destroying hundreds of olive trees and large area of farm land.
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