President Donald Trump made his first global trip since becoming president, at the end of May 2017.
Trump had just visited Israel and the Palestinian areas.
"The president was very forceful in his encouragement to both of them to be serious about approaching these discussions in the future and recognize you have to compromise", Tillerson said in Rome, where he was accompanying Trump on his first overseas trip as president.
"I intend to do everything I can to help them achieve that goal", Trump said after meeting Abbas, speaking with the 50th anniversary of Israel's capture of territories that Palestinians seek for their own state approaching early next month. Both sides will face tough decisions.
"I had a meeting this morning with President Abbas and can tell you that the Palestinians are ready to reach for peace", Trump said in a speech at the Israel Museum in Jerusalem.
Michael Oren, a former Israeli ambassador to Washington, told AFP he was glad Trump's talk of peace "didn't lock us into a specific formula", referring to the two-state solution.
The short visit in Bethlehem came a day after Trump met Israeli Prime Minister Benjamin Netanyahu, as Palestinians held a general strike in support of hundreds of hunger-striking prisoners held in Israeli jails.
Hamas, the Palestinian Islamist movement that runs the Gaza Strip and which rivals Abbas, said Trump aligned "himself with the politics of the (Israeli) occupier" during his visit.More news: Ariana Grande Suspends World Tour Dates After Bombing at Manchester Concert
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The US President, however, criticized the Palestinian Authority for its funding for Palestinians sentenced by Israel on terrorism charges.
The Trump Administration is looking to resolve that by courting top Labor figure Isaac Herzog from the opposition to try to get him to back the peace process.
"We will always insist on Jerusalem", Rivlin said.
It is the first time a sitting USA president has visited and prayed at the site.
Dr. Yitzhak Yifat, Tzion Karasenti and Chaim Oshri joined thousands of Jews from around the world to mark Jerusalem Day.
"The fate of Jerusalem can't be decided by Trump, for Jerusalem is Arab; Jerusalem is Palestinian, and we decide its fate, not the Americans".
"No matter where we go we see the signs of Iran in the Middle East", Trump said.
Israel continues to seize Palestinian land for Jewish-only colonization and to violently suppress the Palestinian population with no consequences from the United States.