Greenblatt also told Netanyahu that Trump considered steps "enabling the growth of the Palestinian economy and improving the quality of life for Palestinians" to be very important.
Palestinian officials say Trump is poised to offer a "historic" deal to bring Abbas back to the negotiating table, perhaps during a US visit that could come as early as next month. And he implied he wasn't committed to a two-state solution.
While Trump has indicated he would not impose US dictates on Israel, it's uncertain if he plans to carry through on that.
In Ramallah, the de facto headquarters of the Palestinian Authority, feelings toward Trump and his intentions have been positive since the Friday phone call between the two presidents.
Forex - Dollar trims gains ahead of Fed decision, sterling off the lows
The Standard & Poor's 500 index fell 8.02 points, or 0.3 percent, to 2,365.45. "Value exists elsewhere in the world". Bond market interest rates are moving up along with these expectations, pushing bond prices down.
"They [Abbas and Greenblatt] reaffirmed the commitment of both the Palestinian authority and the United States to advance the genuine and lasting peace between Israel and the Palestinians", the U.S. Embassy in Tel Aviv said in a statement. About 600,000 Israelis live in over 230 illegal settlements built since the 1967 Israeli occupation of the Palestinian territories of the West Bank and East Jerusalem al-Quds.
According to Addameer Prisoner Support and Human Rights Association, as of January, 6,500 Palestinians were being held in Israeli prisons, 536 under administrative detention.
In a gesture to Israel, Tuesday's statement said that Abbas committed to "preventing inflammatory rhetoric and incitement" and to "heighten his outreach efforts to the Israeli public".
The two also affirmed the US and Palestinian Authority's joint goal of fighting violence and terrorism.
Sara Connor jailed in Bali, Turnbull's Victorian headache
David Taylor , a dreadlocked DJ who adopted a more sober appearance for the trial, said he accepted the judge's decision. The time Connor has already served will be subtracted from her four-year sentence, a judge said on Monday night.
Greenblatt also met with a number of other Palestinian groups on Tuesday, including a group of entrepreneurs, students in Bethlehem, PA security officials, and residents of refugee camp north of Ramallah.
The statement added that during a conversation lasting more than five hours, Netanyahu and Greenblatt discussed Israel's settlement building.
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".
Marquette will Play Friday in the NCAA Tournament
The Golden Eagles are headed to Greenville as a 10 seed to take on the seven-seeded South Carolina Gamecocks on Friday. The victor of that East Regional opener will likely face No. 2 seed Duke, which opens against No. 15 seed Troy.