Jason Greenblatt's talks with Abbas took place in Ramallah, the Palestinian seat of government, a day after he held a lengthy meeting with Israeli Prime Minister Benjamin Netanyahu in Jerusalem.
Trump also emphasized this approach in a phone call to Palestinian Authority President Mahmoud Abbas last week, telling Abbas according to a White House readout that "a peace agreement must be negotiated directly between the two parties", and that "the United States cannot impose a solution on the Israelis and Palestinians, nor can one side impose an agreement on the other".
Greenblatt reaffirmed Trump's commitment to Israel's security, as well as his desire to help Israel and the Palestinians achieve peace through direct negotiations.
"President Abbas told Mr. Greenblatt that he believes that under President Trump's leadership, a historic peace deal is possible, and that it will enhance security throughout the region".
According to a statement from the Israeli Prime Minister's office, Netanyahu and Greenblatt re-established Israel and the US's joint dedication in promoting a true and lasting peace between Israel and the Palestinians that strengthens stability within the Middle East and Israel's security.
But it comes after Trump cast uncertainty over years of global efforts to foster a two-state solution to the conflict when he met Netanyahu at the White House last month.
The Palestinian gross domestic product now stands at approximately $300 million annually, far less than neighboring Israel's GDP, which is upwards of $12 billion.
In an apparent reference to efforts to come up with guidelines with the USA to govern future settlement construction, Netanyahu said, "I can't tell you we reached an agreement, but i think we heard each other out in a serious and friendly way and I think we will probably conclude this effort".
Channel 2 TV said Netanyahu wants to reach understandings with the envoy on settlement building in some areas, in part to appease pro-settler hardliners in his coalition.
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