Reports have suggested that the Trump team is ready to be less censorious on settlements than the Obama administration, countenancing for instance building in eastern Jerusalem and in settlements that likely would be annexed to Israel in a final status agreement.
Chancellor Angela Merkel is reiterating Germany's long-held support for a two-state solution to the Israeli-Palestinian conflict, and its rejection of Israeli settlements.
The U.S. said that it had "concerns" about Israeli policy, but that the discussions would continue.
Following the meeting with Greenblatt, Abbas's office stated that the Palestinian leader believes "that under President Trump's leadership a historic peace deal is possible, and that it will enhance security throughout the region".
The Americans and Israelis said yesterday that Donald Trump's administration has reiterated its concerns regarding Israel's settlements in the occupied Palestinian territories.
German governments have made strong relations with Israel a top priority ever since World War Two, going to great lengths to make amends for the killing of six million Jews by the Nazis.
NI Assembly to come together to remember Martin McGuinness
His efforts were considered central in bringing about the end to the almost daily acts of violence carried out by the IRA. Following the historic meeting, Mr McGuinness met The Queen again in June past year at Hillsborough Castle.
Trump's Middle East envoy, Jason Greenblatt, who recently returned from a visit to the region, led the US delegation in what were described as "intensive discussions" with Israeli Prime Minister Benjamin Netanyahu's chief of staff Yoav Horowitz and foreign policy adviser Jonathan Schachter.
"The sharp increase in settlement construction sends a clear message to the Palestinians and to the global community that Israel is not interested in a two-state solution", Peace Now said.
"Many of the advancements that were made in the past three months will further sever the territorial contiguity of a future Palestinian state and accelerate the fragmentation of the West Bank", said Mladenov of settlements, adding that they were "one of the main obstacles to peace".
The Palestinians want an independent state in the West Bank, Gaza and East Jerusalem.
But Israeli Prime Minister Benjamin Netanyahu has been reluctant to stop settlement building, and his leadership is facing a challenge from the right wing that is pushing for increased building and even annexation of parts of the West Bank. Israel disagrees, citing historical and political links to the land, as well as security interests.