It's an achievement that has proved elusive for many U.S. presidents, yet continues to be a key objective.
Aaron David Miller, a veteran peace negotiator for both Republican and Democratic administrations, said about Trump on Twitter recently, "Never in decades of involvement have I heard a U.S. president more confident with less prospect." Another longtime Middle East diplomat, Robert Danin, replied to Miller on Twitter: "But have you seen one less confident with greater prospect?"
"It’s something that I think is, frankly, maybe not as difficult as people have thought over the years," Trump quipped during Palestinian President Mahmoud Abbas' visit to the White House earlier this month.
"Throughout my lifetime, I've always heard the toughest deal to make is the deal between Israelis and Palestinians," he said during a brief joint appearance with Abbas, "Let's see if we can prove them wrong."
The 82-year-old Abbas has participated in several past negotiations and signed the Oslo Accords in 1993.
"With you, we now have hope," Abbas told Trump in English.
And Trump told Abbas, "I want you to be the Palestinian leader to sign the final agreement with Israel."
Historically, Washington’s approach has been, "We know what the final deal will look like, we just have to get the two parties there," according to Jonathan Schanzer, a research fellow with the Foundation for Defense of Democracies in Washington, D.C. The new thinking, he told reporters recently, seems to say, "We want a deal but we don't know what that final framework will look like."
The Palestinians have little to lose, analysts say, and Trump has already exceeded their expectations just by extending an invitation to the White House, the first Abbas has received in three years.
Israeli Prime Minister Netanyahu was invited before Abbas to the White House, visiting in February and holding a joint news conference with President Trump.
"Bibi," Trump said at the time, using the prime minister's nickname, "and I have known each other for a long time -- smart man, great negotiator."
"I'm looking at two states and one state, and I like the one both parties like," Trump said at the joint news conference with Netanyahu. "I can live with either one."
But neither Trump, nor Netanyahu delved into details.
"Let us seize this moment together," Netanyahu said, "Let us bolster security. Let us seek new avenues of peace."
During his meeting, Abbas pitched the same platform Palestinians have presented for years.
"Mr. President," Abbas said, "our strategic option, our strategic choice is to bring about peace based on the vision of the two-state -- a Palestinian state with its capital of East Jerusalem that lives in peace and stability with the state of Israel based on the borders of 1967."
Last week, standing next to Abbas, Trump repeated more than once, "we will get it done."
"But we can’t afford another big initiative that will fail," he said.
Here is a look at the important milestones in the last four decades of peace efforts:
The Camp David Accords were signed by Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin after 12 days of intense talks initiated by U.S. President Jimmy Carter.
What was agreed upon? A self-governing Palestinian authority would be established in the West Bank and Gaza and Israeli troops would withdraw from the two occupied territories once the authority was elected. The two won a Nobel Peace Prize for negotiating the agreement.
Later, in 1979, Egypt recognized the state of Israel after Israel pulled out of the Sinai. This was the first recognition of Israel by a major Arab country.
1991: Madrid Peace Conference
Why was it important? Madrid set out the peace process framework and laid the groundwork for Israel and the PLO to start secret negotiations, which eventually led to the Oslo Accords.
1993: Oslo Accords Signing
What was agreed upon? Broken into three phases, the accords mandated that Israeli troops withdraw from Gaza and the West Bank and that a Palestinian interim self-governing authority -- the Palestinian National Authority (PA) -- be established. The PA would rule for five years, after which more land transfers would occur. In an exchange of letters, Arafat recognized the state of Israel while Rabin recognized the PLO as the "representative of the Palestinian people." The thorniest issues were never tackled and so-called final status talks never concluded.
2000: Camp David Summit
President Clinton invited the head of the PA Yasser Arafat and Israeli Prime Minister Barak for talks at Camp David to conclude the Oslo process, but no deal was inked. There was no agreement on the final status issues, on a formula to share Jerusalem or ways to address Palestinian refugees.
President Clinton initiated another round of talks in Washington, Cairo and Taba, Egypt but again, no deal was reached. The second intifada, or Palestinian uprising against Israel, was escalating, and Israeli Prime Minister Ehud Barak was in the midst of a heated election campaign and said he couldn't bind the future government of Israel to proposals from the talks. In February 2001, Ariel Sharon was elected and peace talks between the two parties broke down.
2002: Arab Peace Initiative
This plan was proposed at the height of the second intifada by Saudi Arabia at a March 2002 Arab League summit in Beirut. It mandated Israel withdraw to the ceasefire lines of June 1967 and that a Palestinian state would be set up to include Gaza and the West Bank. Arab countries would recognize the state of Israel in return. The United Nations, the European Union and the U.S. all expressed support for the plan.
The plan has continued to surface in discussions, but factions in both the Israeli and Arab camps have objected throughout the years. When the plan was re-endorsed by the Arab League in 2007, U.N. Secretary General Ban Ki-Moon said: "The Arab peace initiative is one of the pillars of the peace process ... it sends a signal that the Arabs are serious about achieving peace." Most recently, Abbas said this spring that the Arab League will stress its commitment to the peace initiative.
The "Roadmap" plan was designed by the so-called Quartet, the U.S., Russia, the EU and the U.N. In the first phase, both the Israelis and the Palestinians would issue statements supporting the two-state solution.
What was on the table? The Israelis would stop expanding settlements and limit military actions while the Palestinians would put an end to violence, create a constitution and hold elections. In the second phase, a Palestinian state would be created with provisional borders. Discussion of the final status issues would take place in phase three. The plan has not yet been executed, but remains a reference point for future negotiations.
2003: Geneva Accord
In December 2003, Yossi Beilin, one of the Israelis behind the Oslo Accords teamed up with Yasser Abed Rabbo, the former Palestinian information minister, to present an informal peace deal. The agreement said that Palestinians should give up their right to return. In exchange, Palestinians would get the West Bank, almost in its entirety. East Jerusalem would be the capital of a future Palestinian state while Israel would control the Western Wall in Jerusalem’s Old City.
President George W. Bush hosted peace talks at the U.S. Naval Academy in Annapolis, Maryland. Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas participated with representatives of the U.S., Russia, the EU, the U.N. and Arab countries, including Syria. The Israelis and Palestinians issued a statement saying they agreed to participate in negotiations, aiming for a peace deal by the end of 2008. Regular talks were held, but no agreement was reached. Negotiations halted when Israel launched a military offensive in Gaza in December 2008 and Olmert was replaced by current Prime Minister Benjamin Netanyahu.
In November 2009, President Obama convinced Netanyahu to freeze settlement construction for 10 months. On September 2, 2010 talks resumed between Netanyahu and Abbas, attended by Egypt and Jordan, but no agreement was reached. The two parties met once more in Sharm el-Sheikh, Egypt, before talks were suspended when Israel's settlement freeze came to an end on September 26. The U.S. failed to convince Netanyahu to renew the freeze or to persuade Abbas to return to the negotiating table without an end to the creation of new settlements in the occupied territory.
2013-2014: Shuttle Diplomacy
After nearly three years of stalled talks, with a handful of discreet bilateral meetings in Jordan, Secretary of State Kerry formally initiated a feverish 9 months of negotiations focused on final status issues. He met with Abbas 34 times, and Netanyahu about twice as many times. Negotiators met frequently, all over the world, but talks broke down entirely in April 2014.