Other members of the royal family, such as the Dukes of Gloucester or Kent, cousins of the Queen, have made official visits to Israel in the past.
Prince William will also meet with two Holocaust survivors, Paul Alexander and Henry Foner, both survivors of the Kindertransport rescue effort which helped bring thousands of Jewish children from Europe to Britain during World War II.
"Need to come back with the family for this shot", he said.
According to Israeli website Ynet, Mr Elki described it as "regrettable" Britain had chosen to politicise the royal visit.
On Tuesday, he is to lay a wreath at the Holocaust memorial Yad Vashem, before meeting separately with Prime Minister Benjamin Netanyahu and President Reuven Rivlin.
At Yad Vashem, William signed a guest book in which he noted with pride that his great-grandmother, Princess Alice, had been honoured by the institution as one of "the righteous among the nations" for sheltering Jews in her home in Greece during the Holocaust.
Prince William will then attend an event in central Tel Aviv where Tel Aviv Mayor Ron Hulda will be present, and finish his day at UK Ambassador David Quarrey's residence in Ramat Gan. "And he really wants to get under the skin of the country", Quarrey added.
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The royal itinerary managed to anger Israeli politicians by mentioning Jerusalem as being part of "the Occupied Palestinian Territories".
CNN reports that William is also expected to visit Jerusalem's Old City, the Mount of Olives and the Church of St. Mary Magdalene in the Garden of Gethsemane. Jerusalem Affairs Minister Zeev Elkin - who is running for mayor of the city in this year's elections - called the reference a "distortion" that can not "change reality".
Israel seized the West Bank and east Jerusalem from Jordan in the 1967 Six-Day War.
Prince William is now in Israel on his first official visit to the country.
The duke's visit comes during a period of increased tension in the region.
At the ruins of Jerash, William stopped in front of an enlarged photo that showed his wife, the former Kate Middleton, as a child, along with her father and younger sister posing against the backdrop of the site.
William was reportedly disappointed to miss the England v Panama game on Sunday afternoon as he was travelling to Jordan.