"I am truly hopeful that America can help Israel and the Palestinians forge peace and bring new hope to the region and its people", Trump said during a joint appearance with Abbas.
"Surely there is no crime more reprehensible than the murder of children", he said, adding: "This is a direct attack on young people everywhere, on freedom everywhere".
"They would think that's a great thing". I will call them, from now on, losers. "We can not stand a moment longer for the slaughter of innocent people", Trump said.
He then appeared to put Prime Minister Benjamin Netanyahu somewhat on the spot.
In his remarks Tuesday morning, Trump called for an end to violence carried out by "terrorists and extremists".
Trump also paid a visit to Yad Vashem, Israel's national Holocaust memorial, where he called the Nazi extermination of six million Jews "the most savage crime against God and his children". And I mean completely obliterated.
'We reaffirm our position to accept the two-State solution along the 1967 borders, that of Palestine with its capital in East Jerusalem, living side by side with Israel, in peace and security and as good neighbors, as well as the resolution of all issues on the basis of global law, ' Abbas said. We all know that.
"Israelis and Palestinians can make a deal but even as we work towards peace we will build strength", Trump added. "Both sides will face tough decisions", he said.
Trump labelled Bethlehem, "a precious city" and said he intended "to do everything he could" to achieve a peace agreement between the Israelis and Palestinians.
Abbas said he was enthusiastic about "keeping the door open to dialogue with our Israeli neighbours".
Mr. Netanyahu said he was heartened to hear Mr. Abbas condemn the attack in Manchester. The Islamic State jihadist group has claimed to be behind it.
To applause from an audience of Israeli political and other leaders, the United States president delivered an uncritical paean of praise to Israel.
Instead of a complete Israeli settlement construction freeze, the Palestinian leadership in Ramallah may be asked to accept a settlement slowdown, analysts say.