Trump's son-in-law and senior White House adviser Jared Kushner and US Middle East peace envoy Jason Greenblatt are in Israel as part of a regional push for the American leader's new peace plan.
The Duke of Cambridge is scheduled to meet both Israeli and Palestinian leaders, including Israeli Prime Minister Benjamin Netanyahu, President Reuven Rivlin, and Palestinian Authority President Mahmoud Abbas.
Kushner says the plan is "almost done", but offered scant details aside from the promise of economic prosperity.
Prince William on Sunday praised "historic ties and friendship" with Jordan and the kingdom's commitment to Syrian and Palestinian refugees, as he began a historic five-day tour that also includes Israel and the Palestinian territories.
Specifically, Kushner recommended to the Palestinian people, "Show your leadership that you are supporting efforts to achieve peace, let them know your priorities and give them the courage to maintain an open mind".
Amru also expressed doubt with regard to the PA leadership's ability to withstand potential sanctions imposed by the USA should the Palestinians reject the Trump peace plan out of hand.
Sources close to Abbas have apparently revealed that Saudi Arabia and Jordan are among those which have given the green light to talks with the USA administration about the deal, which it is said will end the Israeli-Palestinian conflict.
Abbas and the Palestinian leadership have refused to meet with Trump's team following his decision in December to recognise Jerusalem as the capital of Israel and to move the US Embassy there.
Ahead of William's arrival, the official schedule's reference to east Jerusalem as "in the Occupied Palestinian Territories" sparked anger among right-wing Israeli politicians.
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"The Arab countries made it clear that their position remains clear, namely that a two-state solution should be based on worldwide resolutions [pertaining to the Israeli-Arab conflict]", he added.
The Israeli-Palestinian conflict typically looms large, even during largely ceremonious visits, and William will have to maneouver carefully to avoid missteps.
The Jordanian prince then drove William to a technology-focused event for young people linked to the Crown Prince Foundation.
Israel captured east Jerusalem from Jordan in the 1967 Middle East war and annexed it in a move not internationally recognised.
The Palestinian leadership see East Jerusalem as their future capital, insisting the status of the disputed city is an issue to be negotiated between them and the Israelis.
William is visiting a region where three decades of British rule between the two world wars helped establish some of the fault lines of today's Israeli-Palestinian conflict. In 1917, Britain's then-foreign minister Arthur Balfour signed the Balfour Declaration, which played a key role in the creation of the state of Israel by announcing the UK's backing for the establishment within Palestine, then a region of the Ottoman Empire, of "a national home for the Jewish people".
The second marriage of the late King Hussein was to a British citizen, Antoinette Gardiner, who took the title Princess Muna and is the mother of the current monarch, King Abdullah II.
The British prince is expected to visit a Roman settlement where his wife, the Duchess of Cambridge, was photographed with her father in the 1980s. On Sunday evening, William delivered a speech during a reception hosted by the British Embassy in Amman.