(AFP) - Britain's Prince William paid a sombre visit to Israel's Holocaust memorial on Tuesday then took part in a seaside soccer game, tasting two of the country's many faces.

Wearing an open-necked shirt and sunglasses, he strolled along the sunny Mediterranean shoreline in Tel Aviv chatting with surfers about marine pollution.

"Beautiful beach, I should have brought my swimsuit," he remarked.

In the mixed Jaffa neighbourhood, he joined Arab and Jewish youngsters in a football kick-about organised by the Peres Centre for Peace in a programme to encourage inter-communal understanding, scoring penalties against a 13-year-old goalkeeper.

He waved to a group of women outside the sports ground who called through the fence, "Prince William we love you, we love Diana," referring to his late mother.

Coming at the start of the first official trip by a British royal to both Israel and the Palestinian territories, it was in striking contrast to his earlier visit to the Yad Vashem Holocaust memorial in western Jerusalem.

There, he wore a dark suit and a black Jewish skullcap as he rekindled the eternal flame and laid a wreath at the memorial as a youth choir sang.

The 36-year-old, who is the second in line to the British throne, also toured the museum at the site perched on a forested hillside.

His visit comes at a particularly sensitive time after US President Donald Trump recognised Jerusalem as capital of Israel, outraging Palestinians and sparking deadly clashes on the border with Gaza.

Britain governed the region under a League of Nations mandate for almost three decades until Israel's independence 70 years ago, and is still blamed by both sides for sowing the seeds of the ongoing conflict.

William met with two Holocaust survivors, Paul Alexander and Henry Foner, who as children had escaped from Nazi Germany to Britain as part of the "Kindertransport" programme.

"We must never forget the Holocaust," the prince wrote in the visitors' book in neat italic script.

- 'True horrors' of Holocaust -

"We all have a responsibility to remember and to teach future generations about the horrors of the past so that they can never reoccur."

While in Jerusalem, William will also visit the grave of his great grandmother, Princess Alice, who was honoured as among the "Righteous among the Nations" by Yad Vashem in 1993 for sheltering Jews in Greece from the Nazis during World War II.

"I am honoured that my own great-grandmother is one of these Righteous among the Nations," he wrote in the book.

He later met Prime Minister Benjamin Netanyahu and his wife Sara and then called on President Reuven Rivlin, where he spoke of the deep impression his visit to the Holocaust memorial had made upon him.

"I had a very moving tour round Yad Vashem this morning which really taught me quite a lot more than I thought I already knew about the true horrors of what happened to the Jews in the war," he told Rivlin in front of journalists.

William arrived in Israel from Jordan on Monday evening without his wife Kate, the Duchess of Cambridge, who gave birth to their third child two months ago.

He is staying in Jerusalem at the King David Hotel, former headquarters of the British administration during the mandate in Palestine before the creation of the State of Israel in 1948.

On Wednesday he is scheduled to meet Palestinian president Mahmud Abbas in the occupied West Bank city of Ramallah, before meeting Palestinian refugees and young people.

"I know that you are going to be meeting president Abbas," Rivlin told him.

"I'd like to send him a message of peace and tell him that we have to find a way together to build confidence as a way to build understanding."

- 'Not a political visit' -

On Thursday, he is to complete his stay by visiting historical and religious sites in Jerusalem.

"We know this is not a time when we can celebrate progress in the Middle East peace progress, but we believe that engagement is just as important in challenging times as it is in good times," Philip Hall, Britain's consul general in Jerusalem, said on Monday.

"We know some of the politics are difficult, but this is not a political visit."

Israel defines Jerusalem as its "eternal and indivisible" capital, while the Palestinians see east Jerusalem as the capital of their future state.

The Israelis seized the West Bank and east Jerusalem from Jordan in the 1967 Six-Day War.

Some right-wing Israeli politicians have criticised the fact that William's visit to east Jerusalem is being organised by the British consulate-general, which deals with the Palestinians.

But as the prince arrived at Rivlin's official residence in a limousine flying the royal standard, residents of apartment buildings opposite crowded their balconies, cheering and applauding enthusiastically.

© Agence France-Presse