When Pope Benedict XVI pays his respects to the six million Jews killed in the second World War at the Yad Vashem holocaust memorial in Jerusalem tomorrow night, he won't actually tour its stunning museum, inaugurated just four years ago.

The Vatican is at pains to make clear that this simply reflects the multiple demands already being made on the 82-year-old pope during his long-awaited first tour of the Holy Land. But it also means he will be spared a sight of the museum's short, but for the Roman Catholic hierarchy, highly sensitive notice questioning the wartime role of his most controversial predecessor of modern times, Pope Pius XII.

The Vatican stresses that Benedict's first trip here as pope is predominantly a personal pilgrimage. He will hold masses in Jerusalem, Bethlehem and Nazareth, and the warm welcome he will receive is not in doubt. But there is almost nothing about a papal visit here that does not touch a nerve. There are taxation and property disputes with Israel; there are pressures faced by Christian Palestinians. In deference to the Israeli authorities, the pope will not now meet the mayor of the Israeli Arab town of Sakhnin, much criticised on the Israeli right for his opposition to this year's military assault on Gaza. And plans have been dropped for the pontiff to use a platform in a Bethlehem refugee camp which would have sent images across the world of him standing next to the West Bank separation wall.

Given that some Muslims will be uneasy about his controversial 2006 speech quoting a text depicting the Prophet Mohammed as a man of violence, and some Jews about his spell in the Hitler youth – which he has explained was enforced – and his perceived initial leniency towards the Holocaust-denying priest Richard Williamson, it's easy to see the potential for controversy to simmer.

The issue of Pius XII, whom Benedict has described as a "great" churchman is one case in point. The Yad Vashem notice succinctly summarises the argument that Pius failed to take a moral lead against Hitler's extermination of the Jews, or even endorse the Allied declaration in December 1942 condemning it. And that finally when Jews were deported from Rome to Auschwitz, "the pope did not intervene". The 12-line account in Yad Vashem goes to the heart of a still-resonant dispute between most Israeli – and many other – Holocaust scholars and the Vatican.

Pope Pius was a vigorous anti-communist and the concordat he signed as Vatican secretary of state with Franz Van Papen in 1933 followed an earlier meeting with Hitler's vice chancellor and Hermann Goering at which, by Van Papen's account, the future pope remarked "how pleased he was the German government now had at its head a man uncompromisingly opposed to communism and Russian nihilism in all its forms".

An early enthusiasm for Hitler does not, of course, convict Pius of later indifference to the fate of the Jews. But what is not in dispute is Pope Pius's public reticence on the Holocaust, maintained despite numerous attempts by Allied diplomats and many of his own brave prelates and priests to persuade him to speak out.

Pope Pius's defenders say he worked hard behind the scenes to save Jews. Last September, Pope Benedict himself praised Pius for his "courageous and paternal dedication" to that task and argued that there was plenty of evidence to show it. But he produced no new documents to back up his claim.

Which is the problem. Avner Shalev, director of Yad Vashem, says that it is always "open to new facts and to revising our views in the light of research". But to meet its high academic standards, there is a need for documentary evidence and, in particular, papers in the Vatican archive which remain secret after more than six decades. The archives run only up to 1939, and the one volume of records since published by the Vatican on the issue were selected from a huge number of documents. Shalev welcomes a new joint Jewish-Catholic academic commission to "widen the vision and the understanding of a very difficult period of history", as the apostolic nuncio to Israel, Monsignor Antonio Franco, put it last week.

But Shalev argues there is no substitute for making the documents fully available. "The archive is crucial," he says. Defenders point out that some Roman Jews were hidden in monasteries and churches as another 1,000 were deported to their deaths in the autumn in 1943.

"They say this cannot be explained without there having been a direction by the pope," says Shalev. "But this they have to prove." Particularly since the German ambassador to the Vatican at the time, Baron Ernst Von Weizsacker, reported that Pius had "done everything he could in this delicate matter not to strain relations with the German government". Pius's defenders say Weizsacker was protecting the pope from Nazi reprisals. But Pius did not speak out against the deportations.

Towards the end of the war, the pope did appeal to the Slovakian and Hungarian regimes to halt the deportations. But even his 1942 Christmas message deploring persecution for reasons of faith or race did not mention the Jews – or Poles.

For leading Hebrew University holocaust historian Yehuda Bauer, writing in The Tablet, the pope's failure was moral and theological. Contrasting his stance with those of other Catholics who risked or lost their lives saving Jews, Prof Bauer wrote: "Had he spoken out, he probably would not have saved a single Jew, but he might have saved his soul – according to the belief system he genuinely believed in."

Having been told informally that Pope Benedict would like to open the archive within the next five years, "or even accelerate it a bit", Shalev argues that "he would gain a lot" by making a public and irreversible statement to that effect ahead of his visit. Shalev, who will warmly welcome the pope to Yad Vashem tomorrow, fully recognises his long and strongly stated desire to bring the church and Jewry closer together. And he has no wish to labour the pope's youthful past, or doubt his explanation for it. Shalev acknowledges that in contrast to Benedict's immediate predecessor John Paul II, a Pole who saw the regime from the angle of the victims, Benedict saw it "from a different angle". That in turn, says Shalev, lends "a special sensitivity" to his words.