Palestinian Authority President Mahmoud Abbas met with an envoy from President Trump on Tuesday and told him that a peace deal is possible under the new president.
Greenblatt is set to meet Abbas in the West Bank on Tuesday.
Trump appears to have adopted friendlier positions toward Israel than his predecessor, including a vague stance on Palestinian statehood and a more lenient approach to settlements.
Palestinian leaders have expressed interest in cooperating with the U.S. and Israel to improve the Palestinian economy, but have stressed that such efforts need to be a part of a plan to establish an independent Palestinian state. The contact came nearly a month after Netanyahu was warmly received by the president in Washington after years of friction with the Obama administration.
Before taking office, Trump named Greenblatt, his company's top lawyer, as his special negotiator for trade deals and other talks and his adviser to the Middle East and special representative for worldwide negotiations.More news: Alabama's unemployment rate is third highest in the nation
He made the trip "to do a lot of listening, discussing the views of the leadership in the region", acting State Department spokesman Mark Toner told reporters Monday in Washington, calling it "the first of what will become many visits".
A poll released earlier in the day showed widespread skepticism on the part of the Palestinian public, with the vast majority believing that Trump's policies will lead to more tensions or to stagnation.
In a tweet following the discussion, Greenblatt said, "President Abbas & I discussed how to make progress toward peace, building capacity of Palestinian security forces & stopping incitement".
"I'm looking at two-state and one-state, and I like the one that both parties like".
The statement added that Netanyahu and Greenblatt discussed Israel's settlement building "with the hope of reaching a formula that will aim to promote peace and security". He promised to move the U.S. Embassy from Tel Aviv to disputed Jerusalem, a move favored by Israel and bitterly opposed by the Palestinians, and signaled much greater tolerance for Israeli settlement construction on occupied lands. At that meeting, Trump broke with decades of US policy by saying he was not bound to a two-state solution to the conflict and would be open to one state if it meant peace.