'Making peace.will not be easy - we all know that, ' Trump stated. Both sides will face tough decisions.
Israeli Prime Minister Netanyahu offered Trump a reality check.
Mr Abbas is an unpopular leader, according to polls, and the Palestinian political landscape is split between his Fatah party and Hamas, the Islamist movement that is in control in the Gaza Strip and opposes negotiations with Israel.
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"The conflict is not between religions", Abbas said.
On Monday, Trump noted that his administration's two leaders on the issue - Middle East envoy Jason Greenblatt and Israeli Ambassador David Friedman - both left behind plum private sector jobs due to their belief in the possibility of peace.
President Trump, on his tour of the Middle East, condemned the suicide bomber who detonated explosives at the Manchester, England, arena where Ariana Grande was performing, killing 22 and injuring 59 others. I am telling you - that's what I do - they are ready to reach for peace. They'd think that's a great name.
"I will call them from now on losers because that's what they are", he said. And we'll have more of them. "But they're losers. Just remember that". Trump is to meet Abbas at the presidential palace in Bethlehem, which holds deep significance as the site where Christians believe Jesus was born. A banner hung in the city said "the city of peace welcomes the man of peace" along with photos of Abbas and Trump.
Abbas called on Israel to accept the demands for better conditions by hundreds of imprisoned Palestinians who have been on a hunger strike for 37 days. He said that the Palestinians' problem is with the occupation and Israel's position of not recognising the Palestinian state. "Today, this right, ultra-right-wing government has frozen settlement construction and has given Palestinians construction in Area C", Herzog said, referring to recent moves by Netanyahu's conservative governing coalition.
After the first couple boarded by they were followed by daughter Ivanka Trump, her husband Jared Kushner and Secretary of State Rex Tillerson.
He became the first sitting U.S. president to visit the site in the Israeli-annexed east of the city. Trump pointed to Israel's Iron Dome missile defense program, which has been in operation for more than a decade, as well as David's Sling, created to intercept medium- and long-range missiles, which was first tested by the Israeli Defense Forces in 2012. The US has never recognized Israeli sovereignty over the Old City seized in the 1967 war.