When Netanyahu met with Trump last month in Washington it was chose to set up a mechanism, led by Greenblatt and ambassador to the US Ron Dermer, to develop agreed upon guidelines between the US and Israel about where construction in the settlements will be permitted.
Greenblatt's visit to the region comes just days after Trump spoke by phone with Abbas in a call in which the American president invited the Palestinian leader to meet at the White House.
Netanyahu was one of the first world leaders to visit Trump in Washington, D.C. last month, as the new USA president gave a press conference in which he said he was not wedded to the idea of a two-state solution.
The US' Ambassador to the United Nations, Nikki Haley, later said the US remained committed to a two-state solution and anyone who believed Washington was abandoning the policy did so in "error".
He has also sparked concern among Palestinians and others by pledging during his campaign to move the U.S. embassy in Israel from Tel Aviv to Jerusalem, whose status is one of the thorniest issues of the conflict.
The worldwide community generally supports a two-state solution to the Israeli-Palestinian conflict in order to preserve the Palestinian identity and Israel's unique status as a Jewish-majority state.More news: Surprising Israel's World Baseball Classic run ends with loss to Japan
Settlements are seen as illegal under global law and a major stumbling block to peace as they are built on land the Palestinians see as part of their future state.
Trump had called on Obama to veto the resolution.
According to the release, Trump stressed that Washington will work closely both with Palestinian and Israeli leadership to make a peace deal possible. The statement said that the two men discussed the issue of settlement construction "in the hope of coming up with a formula that will lead to the goal of peace and security".
However, the President's sincerity in wanting to secure peace in the region - demonstrated by the fact his son-in-law Jared Kushner has been put in charge of brokering a peace deal - has caught many in the region who assumed that Mr Trump's friendliness would leave the Netanyahu coalition government to its own devices off guard.
Following the meeting with the Israeli PM on Monday, Greenblatt tweeted that they "discussed regional situation, how progress towards peace with Palestinians can be made & settlements".