On Thursday, he is to complete his stay by visiting historical and religious sites in Jerusalem.
Prince William visited a sentimental spot on the second day of his five-day tour of the Middle East.
But tradition and history will mark many of his stops in an area fought over for centuries and once administered by colonial Britain in the final days of its empire.
With a visit to Ramallah in the Occupied Palestinian Territories also planned, where he will meet Palestinian Authority president Mahmoud Abbas, the tour will be a tough diplomatic test for the second-in-line to the throne, who will have to avoid straying into regional politics.More news: Lionel Messi's Argentina have shot at World Cup redemption
According to Hello! during a reception at the British ambassador to Jordan's residence in the capital of Amman, Rania Malki, chief executive of Save The Children in Jordan, told Prince William that she knew the house that the Middleton family had lived in, as it's now the home of her children's paediatrician.
William's hugely symbolic trip is something he has been keen to do and will see him sit down for talks with Israeli prime minister Benjamin Netanyahu and President Reuven Rivlin.
Kate, also 36, is on maternity leave from royal duties after giving birth to the couple's third child, Louis, in April.
Kate is aged four in the picture, while Pippa is around two.
The visit comes as Israel has celebrated 70 years since it was created. More than 90 people were killed.More news: New AirPods, Apple noise-cancelling headphones pegged for 2019
Israel seized the West Bank and east Jerusalem from Jordan in the 1967 Six-Day War.
The trip is at the behest of the British government.
The prince's trip was announced in March and welcomed by Israeli and Palestinian officials.
Yad Vashem Chairman Avner Shalev, who guided the Duke of Cambridge through the museum's exhibitions detailing Nazi Germany's genocide of 6 million Jews during World War II, said the prince was very curious and emotional as he stopped to inquire about various elements of the Holocaust.
In a private 1994 visit to Yad Vashem, Prince Philip, the Duke of Edinburgh, planted a tree there in his mother's honour.More news: 'Permit Patty' calls cops on girl selling water in San Francisco
William's itinerary includes visits to Tel Aviv and adjacent Jaffa, where he will meet young Jews and Arabs and view high-tech products made by Israeli start-ups.