President Trump meets with Palestinian Authority leader Mahmoud Abbas at the White House on Wednesday, May 3, 2017. (Screenshot from White House video)

(CNSNews.com) – President Trump expressed optimism Wednesday that he may succeed where predecessors have failed in mediating an Israeli-Palestinian peace agreement, even as visiting Palestinian Authority leader Mahmoud Abbas recited the same list of positions rejected by Israeli governments in past negotiations.

“Over the course of my lifetime I’ve always heard that perhaps the toughest deal to make is the deal between the Israelis and the Palestinians,” Trump told reporters after their Oval Office meeting. “Let’s see if we can prove them wrong.”

At the beginning of a working lunch with Abbas’ delegation, Trump said of a Mideast peace deal, “It’s something that I think is frankly, maybe not as difficult as people have thought over the years, but we need two willing parties.”

“We believe Israel is willing. We believe you’re willing,” he added to Abbas, “And if you both are willing, we are going to make a deal.”

In his remarks to the press, Abbas called for a Palestinian state based on the 1967 “borders,” with East Jerusalem as its capital, and said the issue of Palestinian refugees must be resolved “according to the terms of international law.”

Israeli leaders have called the so-called “1967 borders” – the 1949 armistice lines that were in place up until the June 1967 Six Day War – “indefensible.” A return to those boundaries would deprive Israel of the entire West Bank including the strategic Jordan Valley along the border with Jordan, and leave Israel at its narrowest point nine miles wide between “Palestine” and the Mediterranean Sea.

Jerusalem, which Israel claims as its age-old, united and “indivisible” capital, remains a key hurdle in the path of a negotiated settlement. So too does the Palestinian insistence on the “right of return” of Arab refugees who left present-day Israel in 1948 and their descendants, now numbering some five million, according to the U.N. (Israel’s total population is 8.6 million, 1.8 million of whom are Arabs.)

Abbas demanded that Israel recognize a Palestinian state “just as the Palestinian people recognize the state of Israel,” but he pointedly did not define Israel as a Jewish state – something Israeli Prime Minister Binyamin Netanyahu has been calling for since a landmark 2009 speech in which he conditionally endorsed Palestinian statehood.

The P.A. “needs to recognize the state of the Jews just like they are demanding from us that we recognize the state of the Palestinians,” Netanyahu has stated; Abbas has long rejected the demand.

Israel for years has been calling on the P.A. to end the incitement to violence in official media programming, including children’s shows, and in school textbooks, as tracked by groups like Palestinian Media Watch and the Middle East Media Research Institute.

Trump raised the issue in his public remarks, saying that “there can be no lasting peace unless the Palestinian leaders speak in a unified voice against incitement to violate, and violence, and hate.”

Abbas implicitly rejected the accusation, telling Trump, “We are raising our youth, our children, our grandchildren on a culture of peace.”

Abbas, whose electoral mandate expired in January 2009 but has been extended by decree ever since, said it was time for Israel “to end its occupation of our people and of our land,” declaring that the Palestinians are “the only remaining people in the world that still live under occupation.”

Others around the world whose territories are occupied – but whose cases are seldom raised at the United Nations – include Kurds in south-eastern Turkey, the people of Tibet and Uighurs in Xinjiang in western China, and the inhabitants of Moroccan-occupied Western Sahara, Turkish-occupied northern Cyprus and Indonesian-occupied West Papua.