But in both the West Bank and Gaza, Palestinians held angry protests against the US president's visit.
On Monday, Mr Trump stressed the strong bonds between the US and Israel.
Speaking about the prospect of a peace deal with the Palestinians, he said: "I've heard it's one of the toughest deals of all."
But he added that he had a "feeling that we're going to get there eventually".
He said he hoped his meeting with Mr Abbas, in Bethlehem, could be "useful and fruitful".
Later on Tuesday Mr Trump will return to Jerusalem to visit the Vad Yashem Holocaust memorial and make a speech at the Israel Museum.
The two-day visit to Israel and the Palestinian territories forms part of Mr Trump's first foreign trip as US president.
President Trump sees himself as a great dealmaker, with the personality to cut through the difficulties that have defeated lesser people.
The only credible ideas still require the creation of an independent and sovereign Palestinian state alongside Israel. The reality is that the Israelis and Palestinians are way apart on the main issues - the future of east Jerusalem, the fate of Palestinian refugees and the borders of an independent Palestine. The two sets of leaders also do not trust each other.
The West Bank, including East Jerusalem, has been occupied by Israel for 50 years. Some of the most influential members of the Israeli government believe the land is a Jewish possession, given by God.
The Palestinians are deeply divided, with Fatah in charge in the West Bank and in Gaza the Islamists of Hamas, who have been condemned by President Trump in the last few days as terrorists.
It is highly unlikely that even President Trump's outsize personality will be enough, on its own, to end a conflict that has lasted more than a century. Making this deal is not about fixing a price - it is about reconciling enemies with radically different world views.
What is the mood in the territories?
On Monday Palestinians gathered to protest against Mr Trump's visit, and over conditions in Israeli prisons, at military checkpoints around the West Bank.
Hundreds of stone-throwing youths clashed with Israeli soldiers firing tear gas and rubber bullets.
At least one person was injured at the Qalandia checkpoint near Jerusalem.
In the Gaza Strip, other Palestinians trampled photos of the US leader and, according to Reuters news agency, burnt an effigy of him.
A "day of rage" has been called for Tuesday by the Palestinian prisoners' committee.
Hundreds of jailed Palestinians have been on hunger strike since 17 April. Activists are hoping to hold up protest banners in Bethlehem on Tuesday to make Mr Trump aware of the action.
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