In a run-down office in the busy centre of Tel Aviv, a group of Israelis are finalising preparations for this year's independence day holiday. But their conversation – switching between Arabic and Hebrew – centres not on celebrating the historic realisation of the Zionist dream in May 1948, but on the other side of the coin: the flight, expulsion and dispossession that Palestinians call their catastrophe – the Nakba.

Maps, leaflets and posters explain the work of Zochrot – Hebrew for "Remembering". The organisation's mission is to educate Israeli Jews about a history that has been obscured by enmity, propaganda and denial for much of the last 66 years.

Next week, Zochrot, whose activists include Jews and Palestinians, will connect the bitterly contested past with the hi-tech present. Its I-Nakba phone app will allow users to locate any Arab village that was abandoned during the 1948 war on an interactive map, learn about its history (including, in many cases, the Jewish presence that replaced it), and add photos, comments and data.

It is all part of a highly political and inevitably controversial effort to undo the decades-long erasure of landscape and memory – and, so the hope goes, to build a better future for the two peoples who share a divided land.

"There is an app for everything these days, and this one will show all the places that have been wiped off the map," explains Raneen Jeries, Zochrot's media director. "It means that Palestinians in Ein Hilweh refugee camp in Lebanon, say, can follow what happened to the village in Galilee that their family came from – and they will get a notification every time there's an update. Its amazing."

In a conflict famous for its irreconcilable national narratives, the basic facts are not disputed, though the figures are. Between November 1947, when the UN voted to partition British-ruled Palestine into separate Arab and Jewish states, and mid-1949, when Israel emerged victorious against its enemies, 400-500 Arab villages and towns were depopulated and destroyed or occupied and renamed. Most of them were left in ruins.

Understanding has deepened since the late 1980s, when Israeli historians used newly opened state archives to revisit that fateful period. Key elements of this new history contradicted the old, official version and partially confirmed what Palestinians had always claimed – that many were expelled by Israeli forces rather than fled at the urging of Arab leaders.

Fierce debate still rages over whether this was done on an ad hoc basis by local military commanders or according to a masterplan for ethnic cleansing. The result either way was disastrous.

Zochrot's focus on the hyper-sensitive question of the 750,000 Palestinians who became refugees has earned it the hostility of the vast majority of Israeli Jews who flatly reject any Palestinian right of return. Allowing these refugees – now, with their descendants, numbering seven million people – to return to Jaffa, Haifa or Acre, the argument goes, would destroy the Jewish majority, the raison d'etre of the Zionist project. (Israelis often also suggest an equivalence with the hundreds of thousands of Jewish refugees who lost homes and property after 1948 in Arab countries such as Iraq and Morocco - although their departure was encouraged and facilitated by the young state in the 1950s.)

"There are a lot of Israeli organisations that deal with the occupation of 1967, but Zochrot is the only one that is dealing with 1948," said Liat Rosenberg, the NGO's director. "It's true that our influence is more or less negligible but nowadays there is no Israeli who does not at least know the word Nakba. It's entered the Hebrew language, and that's progress."

Rosenberg and colleagues hold courses and prepare learning resources for teachers, skirting around attempts to outlaw any kind of Nakba commemoration. But the heart of Zochrot's work is regular guided tours that are designed, like the gimmicky iPhone app, to put Palestine back on the map and to prepare the ground for the refugees' return.

On a recent Saturday morning, a couple of dozen Jews and Arabs met at a petrol station on the southern outskirts of Jerusalem and followed a dirt track to al-Walaja, a village of 2,000 inhabitants that was attacked and depopulated in 1948. Zochrot's Omar al-Ghubari pointed out the concrete foundations – all that remains – of a school and marked the spot with a metal sign in Arabic, Hebrew and English, before posing for photographs.

Among those following him was Shireen al-Araj, whose father was born in al-Walaja and fled to Beit Jallah across what until 1967 was the armistice line with Jordan. "I have never given up the idea of going back to al-Walaja," she said. Araj is campaigning against the extension of the West Bank separation wall, part of what she and many Palestinians call a continuing Nakba.

Another participant was Tarik Ramahi, an American surgeon raised in Saudi Arabia by Palestinian refugee parents. Marina, a Jewish social worker, came with her boyfriend Tomer, an IT student. Wandering among the ruins, these unconventional daytrippers attracted some curious glances from Israelis picnicking on the terraces or bathing in the village spring – now named for a Jewish teenager murdered by Palestinians in the 1990s. Claire Oren, a teacher, had a heated argument with two off-duty soldiers who were unaware of al-Walaja's past – or even of the extent of Israel's continuing control of the West Bank.

Nearby Ein Karem – Zochrot's most popular tour – is a different story. Abandoned by the Palestinians in July 1948 (it is near Deir Yassin, the scene of the period's most notorious massacre), it boasts churches, a mosque and fine stone houses clustered around a valley that is choked with wild flowers in the spring. Its first post-war residents were poor Moroccan Jewish immigrants, but it was intensively gentrified in the 1970s and is now one of west Jerusalem's most desirable neighbourhoods.

In 1967, Shlomo Abulafia, now a retired agronomist, moved into a two-room hovel that he and his wife, Meira, have transformed beyond recognition into a gracious Arab-style home set in a charming garden. Relatives of the original owners once visited from Jordan. Like other Israeli Jews who yearn for coexistence with the Palestinians, Abulafia believes it is vital to understand how the other side feels. He worries desperately about the future of his fractured homeland and about his children and grandchildren.

"The Nakba is history for us but a catastrophe for them," he says. "What have we got to lose from recognising the Palestinians' suffering? The two sides are moving further and further away from each other. People live in fear. There is a lot of denial here."

Many other Arab villages disappeared without trace under kibbutz fields and orchards, city suburbs or forests planted by the Jewish National Fund. Arab Isdud became Israeli Ashdod. Saffuriya in Galilee is now Zippori, the town's Hebrew name before the Arab conquest in the seventh century.

Zochrot's bilingual guide book identifies traces of Arab Palestine all over the country – fragments of stone wall, clumps of prickly pears that served as fences, or the neglected tombs of Muslim holy men. The faculty club of Tel Aviv University used to be the finest house in Sheikh Muwannis, once on the northern edge of the expanding Jewish city. Nothing else is left. Manshiyeh, a suburb of Jaffa, lies beneath the seaside Charles Clore promenade.

Palestinians have long mourned their lost land, eulogising it – and in recent years documenting it – with obsessive care. Politically, the right of return remains a totemic demand even if PLO leaders have often said privately that they do not expect it to be implemented – except for symbolic numbers – if an independent Palestinian state is created alongside Israel and Jewish settlers uprooted from its territory. Mahmoud Abbas, the Palestinian president, provoked uproar in 2012 when he said he would not expect to be able to return to his home town of Safed.

Older Israeli Jews like Meron Benvenisti, raised in British-ruled Palestine during the 1930s, have written nostalgically about the forgotten landscapes of their childhood.

"I also identify with the images of the destroyed villages," said Danny Rubinstein, a Jerusalem-born author and journalist. "I do understand the Palestinians' longing and I empathise with it. But I think that Zochrot is a mistake. The Palestinians know, or their leadership knows, that they have to forget Ramle and Lod and Jaffa. Abbas says he can't go back to Safed. They have to give up the return as a national goal. If I was a Palestinian politician I would say that you don't have to remember. You have to forget."

Hopes for a negotiated two-state solution to the conflict between Israelis and Palestinians are fading after the collapse of the latest US-brokered effort, and mutual empathy and understanding are in short supply. But Claire Oren, resting in a shady grove in what was once the centre of al-Walaja, thinks more knowledge might help. "Even if only one Israeli becomes a bit more aware of the Nakba and the Palestinian refugees, it is important," she reflected. "The more Israelis who understand, the more likely we are to be able to prevent another catastrophe in this land."