As Trump told reporters during an appearance with Abbas on Wednesday, "I'm committed to working with Israel and the Palestinians to reach an agreement, but any agreement can not be imposed by the United States or any other nation".
Abbas reiterated the PA position that east Jerusalem be part of a future Palestinian state "based on 1967 lines", adding there must be a just agreement based on the two-state solution. "We need two willing parties", Trump said before a working lunch with Palestinian President Mahmoud Abbas.
Barely two and a half months after having received Israeli Prime Minister Benjamin Netanyahu, the USA president greeted Abbas on the White House lawn, before ushering him into the Oval Office for their talks.
The last round of US-brokered peace talks collapsed in 2014.
He hailed Abbas for signing the Oslo Accords on the White House lawn 24 years ago, recalling that his guest was a signatory to that first agreement and hoping that the PA president would, in due course, be able to sign a final, permanent accord.
Shortly after assuming office, Trump signaled he is not opposed to abandoning the long-sought proposal to end the decades-old conflict, saying he instead prefers an undefined "ultimate deal".
"I believe that we are capable under your leadership and under your courageous stewardship and your wisdom as well as your great negotiating ability".
Abbas promised that Palestinians are raising "our youth... on a culture of peace", and that the Holy Land will become a place "where the three monotheist religions thrive... in an environment of security, peace, and stability and love for all".
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"We are aspiring and want to achieve our freedom, our dignity, and our right to self-determination", said Abbas.
He told Mr Abbas: "We will get it done".
Trump said he had spoken to Israeli Prime Minister Benjamin Netanyahu, adding that he would "do whatever is necessary" to reach an agreement.
But as president, Trump has yet to take steps to fulfill that promise and has declined to lay out a concrete roadmap to an Israeli-Palestinian peace deal. Trump said he has always heard that a peace agreement between Israel and the Palestinians was the "toughest deal" to close.
Abbas called for a two-state solution, which would establish an independent Palestinian nation alongside Israel. A recent poll suggests two-thirds of Palestinians want him to resign, unhappy with the results delivered by what they see as a corrupt PA.
Abbas needs Trump's support to legitimize his power, and Ross encouraged Trump to press Abbas to make concessions, such as ceasing sending money to jailed Palestinians who had killed Israelis.
He quickly reasserted the goal of the creation of a Palestinian state as vital to any rejuvenated peace process.
Both leaders avoided mentioning any specifics on the way forward beyond a United States push to counter incitement and hate rhetoric from the Palestinian side.