Later, the prince will meet Israeli President Reuven Rivlin and Prime Minister Benjamin Netanyahu before heading to coastal Tel Aviv to attend a football game of young Jewish and Arab players.
Prince William is due to visit her tomb on Thursday.
"Yesterday, it was a little bit tricky: I turned up like this on the beach".
Wearing a light blue shirt, dark blue trousers and blue Nike sneakers with a yellow logo, the prince scored two out of three penalty kicks against a 13-year-old goalkeeper.
The duke's visit to Israel and the Occupied Palestinian Territories is the first time a member of the royal family has travelled to the areas at the request of the Government, and something William was keen to do.
The prince's visit comes at a time of heightened tensions in the region, with deadly clashes on the Gaza border following protests as Israel marks its 70th anniversary year, and U.S. president Donald Trump's decision to move the USA embassy from Tel Aviv to Jerusalem.
Britain governed the region under a League of Nations mandate for nearly three decades until Israel's independence 70 years ago, and is still blamed by both sides for sowing the seeds of the ongoing conflict.
"We all have a responsibility to remember and to teach future generations about the horrors of the past so that they can never reoccur".
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 visibly moved as he stopped to inquire about various elements of the Holocaust.
"I am honoured that my own great grandmother is one of these Righteous Among the Nations".
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Prince William may be travelling without his wife in the Middle East but she's clearly not far from his mind. "I was very impressed by how many plastic bottles there were in there".
Prince William, Duke of Cambridge, poses for a picture with soccer teams in Jaffa-Tel Aviv, on June 26.
William will be staying at Jerusalem's King David hotel during his visit to Israel, which has welcomed world leaders, royalty and famous faces from across the globe.
"So, for instance, the first time you meet him you say 'Welcome Your Royal Highness, ' then after that you call him 'Sir, '" Ritz told the Jewish News Online.
"Build confidence as a first step to bring to understanding that we have to bring to an end the tragedy between us that goes along for more than 120 years".
Kensington Palace said in a statement: "The next morning of the 27th will begin back in Tel Aviv, with a visit that we are really looking forward to, but will not be announcing in advance".
Prince William will continue his "non-political" trip of the Middle East, through Jordan, Israel and Palestine, before heading to the Dar Na'mah Centre.
The Israelis seized the West Bank and east Jerusalem from Jordan in the 1967 Six-Day War.
Yet he is likely to rub up against the complicated realities of the Israeli-Palestinian conflict, particularly when he visits the disputed holy city of Jerusalem.
The Greek royal family - Princess Alice was married to Prince Andrew of Greece - had been acquainted with Cohen's late husband, Haimaki, a former member of Greece's parliament.
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29 Juin 2018