The two men met outside the presidential palace in Bethlehem and walked along a red carpet onto its grounds.
Speaking at a joint press conference, Mr Trump said he was committed to achieving peace, but added: “Peace can never take root in an environment where violence is tolerated, funded and even rewarded."
He added: "My thought are with the people of Manchester after this terrible terrorist attack. They were evil losers.
"I won’t call them monsters because they would like that term. They would think that was a great name. I will call them losers from now on. And we’ll have more of them. But they’re losers, just remember that.”
The Palestinian leader asserted that the key to peace was freedom and independence.
He said: "The conflict is not between religions. Respecting religions is an integral part of our faith."
He said the Palestinians "fundamental problem is with the occupation, the settlements, and Israel's failure to recognise Palestine."
Mr Abbas also spoke about the hunger strike by Palestinian prisoners calling on the Israeli government to "meet their humane and legitimate demands”.
Later this morning, Mr Trump will visit Yad Vashem, before heading for the Israel Museum where he will deliver an address. He will then head straight for the airport for his onward flight to the Vatican.
