At talks with Mahmoud Abbas, he spoke of being gratified that the Palestinian leader had committed to taking necessary steps to "fight terrorism".
Israel and the Palestinians have not held peace talks for three years and Mr Trump acknowledges it would be "one of the toughest deals of all" to broker.
This is the last day of the US president's visit to the Middle East.
In both Gaza and the occupied West Bank, Palestinians have held protests against the trip and in support of a hunger strike by Palestinian prisoners in Israeli jails.
On Monday, Mr Trump said he had come to "reaffirm the unbreakable bond" between the US and Israel and that there was a "rare opportunity to bring security and stability and peace" to the region.
He flew to Tel Aviv direct from Saudi Arabia, where at a summit on Sunday he urged Arab and Muslim leaders to work together to "drive out" Islamist extremists.
Mr Trump said he had come to Bethlehem, where the meeting with Mr Abbas was held on Tuesday morning, "in a spirit of hope".
"I am committed to trying to achieve a peace agreement between the Israelis and the Palestinians," he said. "And I intend to do everything I can to help them achieve that goal.
He added the president of the Palestinian Authority had assured him he was "ready to work towards that goal in good faith", and that Israeli Prime Minister Benjamin Netanyahu had promised the same.
Mr Trump also said that he was "gratified" that Mr Abbas had attended the summit in Riyadh and "committed to taking firm but necessary steps to fight terrorism and confront its hateful ideology".
"Peace can never take root in an environment where violence is tolerated, funded and even rewarded," he added, apparently referring to payments made by the PA to the families of Palestinian prisoners and those killed in the conflict with Israel.
Mr Abbas welcomed Mr Trump's "noble and possible mission".
"I would like to reiterate our commitment to co-operate with you in order to make peace and forge an historic peace deal with the Israelis," he said.
The US president began his statement with a condemnation of Monday evening's suicide bomb attack at a concert in Manchester.
"So many young, beautiful, innocent people living and enjoying their lives murdered by evil losers in life," he said.
Later on Tuesday Mr Trump returned to Jerusalem, visiting the Yad Vashem Holocaust memorial.
And in a speech later at the Israel Museum, he reaffirmed that his administration would always stand with Israel.
But he said his trip was "focused on bringing nations together", adding that the Palestinians were "ready to reach for peace".