JERUSALEM – Diving head-first into one of the most intractable conflicts in the world, President Trump continues his attempt to make progress on peace in the Middle East on Tuesday, traveling to Bethlehem to meet with Palestinian President Mahmoud Abbas.

It's part of a carefully constructed theme of Trump's first foreign trip as president. By visiting countries that are the spiritual homes of Islam, Judaism and Catholic Christianity, Trump is seeking to bring a message of unity to people of faith, especially in the fight against terrorism. Trump also plans to visit Israel’s Holocaust Museum, Yad Vashem, and then make a speech at the Israel Museum on Tuesday.

Trump became the first sitting president to pray at Jerusalem's Western Wall on Monday, visiting a site with both religious and political significance as he attempts to broker peace between Israelis and Palestinians.

Wearing a black yarmulke, Trump stood quietly at the wall and slipped a customary prayer into its cracks.

Trump said he was "deeply moved" by his visit to the wall, which came on the first day of his two-day visit to Israel. "Words fail to capture the experience. It will leave an impression upon me forever."

First Lady Melania Trump and daughter Ivanka also prayed at the wall, but did so separately because worship there is segregated by gender.

The geography of the wall, considered Judaism's holiest place of prayer, is fraught with controversy.

During planning for Trump's visit, an American diplomat told Israeli officials that they weren't welcome to accompany Trump to the wall because it was in Palestinian territory — prompting an uproar in Israel. The Israeli government has considered the wall under its jurisdiction since it captured the Old City during the Six Day War in 1967. Muslims view the same compound, which holds the Dome of the Rock and al-Aqsa mosque, as a holy site. Yet the U.S. has not recognized Israel's sovereignty over the area, even as Israel gears up to recognize the 50-year anniversary of the "reunification" of Jerusalem this week.

The incident demonstrates the complicated history of city, where Trump arrived Monday in search of what he has called "the ultimate deal" — an Israeli-Palestinian peace agreement that would finally end decades of failed and frustrating diplomacy. Jerusalem is a central point in that controversy: Israel sees Jerusalem as its undivided, "eternal" capital; Palestinians claim East Jerusalem as the capital of a future state.

Meeting with Israeli President Reuven Rivlin, Trump said the time may be right for a peace accord that has eluded many of his predecessors. Trump cited what he said was "a really good feeling toward Israel" at the American Arab Islamic Summit in Saudi Arabia over the weekend.

"What’s happened with Iran has brought many of the other parts of the Middle East toward Israel, and you could say that if there’s a benefit, that would be the benefit," Trump said.

"Every challenge creates opportunity," Rivlin responded.

"You have a great opportunity," Trump said. "People have had enough. They’ve had enough of the bloodshed and the killing. I think you’re going to see something happen."

However, as he heads into his meeting with the Palestinian leader Abbas, Trump knows there are potential difficulties ahead.

"I heard it’s one of the toughest deals of all," Trump said, intentionally quoting himself. "But I have a feeling we will get there eventually. I hope."

Speaking to reporters on Air Force One, Secretary of State Rex Tillerson said Trump feels now is a "moment in time" when a breakthrough is possible. "I think the president has indicated he’s willing to put his own personal efforts into this, if the Israelis and the Palestinian leadership are ready to be serious about engaging as well," he said.

Much of Trump's first day in Jerusalem was spent in ceremonies both celebratory and somber.

Fresh off a remarkably warm reception in Saudi Arabia, Trump arrived at Ben Gurion International Airport and walked a red-carpeted gauntlet of Israeli dignitaries there to greet him. The display wasn't entirely spontaneous: Israeli media reported that Prime Minister Benjamin Netanyahu made attendance mandatory for all government ministers.

Netanyahu called Trump's flight from Riyadh to Tel Aviv "a historic milestone on the path to reconciliation and peace." Indeed, the Air Force One flight itself was as symbolic as it was historic: It was the first known direct flight allowed between Saudi Arabia and Israel in modern history. Later, Trump toured the Church of the Holy Sepulchre — built on the location where Christians believe Jesus died and was buried.

The visit also comes as the U.S.-Israeli relationship is stressed by revelations that Trump shared sensitive Israeli intelligence with Russia in an Oval Office meeting two weeks ago.

Trump insisted Monday that he never identified Israel as the source of that information, but intelligence agencies worry that details of the plot could allow the Russians to identify where the information came from.