Mazen Faraj and Robi Damelin … each has faced hostility from their own community. Photograph: Sarah Lee for the Guardian

It was only later, after the intense shock had subsided and a heavy pain was starting to bed in, that Robi Damelin was told what her first words were on hearing that her son had been killed: "You may not kill anybody in the name of my child." She says now: "I suppose that was some kind of prediction of what I would do in the future. But I don't know what revenge means. How many people should I kill? Would that bring David back? I was very motivated to find something that would prevent other families experiencing this pain."

In 2002, David, a university student who had been doing his reserve duty in the Israeli Defence Force, was killed by a Palestinian sniper while he was guarding a checkpoint. Damelin, who was running a PR agency in Tel Aviv, could no longer work – it felt meaningless. A group called the Parents Circle Families Forum asked if she would like to join them: set up in 1995 by Yitzhak Frankenthal, whose 19-year-old son was killed by Hamas fighters, it now comprises more than 600 bereaved Israeli and Palestinian families working together to campaign for reconciliation.

"It was quite extraordinary to meet Palestinian mothers and discover this joint pain, and how powerful we could be as a force together to make a difference," she says. "And so I got swept along, and it became more and more my life. And now, apart from my grandchildren, there is nothing else – I have become a very one-dimensional character, absolutely geared to this idea. This latest Gaza mess is just so indicative of the cycle of violence. It's not working for either side. Neither of us can win this battle. All that will happen is there will be more and more broken hearts."

We meet a few hours before the ceasefire ended eight days of violence in Gaza. The issue, says Damelin, is how long it will be until the violence flares up again and another short-term ceasefire has to be negotiated. "Sometimes I can't believe the stupidity of the repetition," she says. It doesn't threaten the unity of the group "because we don't allow this situation to affect who we are.

"We continue to work. The Palestinians from our group continue to come to schools and talk. I'm not sure if I watched the news on Al Jazeera every day I would continue to come and talk about reconciliation, so we think that's a really good indication of the trust within this organisation."

"Sometimes you get very disappointed," says Mazen Faraj, who has been sitting quietly listening to Damelin: "All the work you are doing – and then you find yourself in a new cycle of violence." He was born in a refugee camp in the West Bank, where he still lives with his young family. As a teenager, Faraj and his brothers were imprisoned in Israeli jails several times. In 2002, his father was shot dead by an Israeli soldier.

"Since I was a kid, I have been dealing with the conflict," he says. "It is so hard to live in a country without security, justice, rights. After the loss of my father, I spent a lot of time not knowing what to do. It was a huge feeling. There are options – you can choose revenge and become a suicide bomber, or you can stay at home and die slowly with your memories, or maybe you can really do something useful. To become an extremist is the easy way, but to reach a solution in this conflict through dialogue, and to find understanding, would be more helpful for me."

Joining the group, he says, felt like a rare choice he could make in his life. "When you are living under Israeli occupation, you can't decide anything. The work with the Parents Circle, I have chosen it and I decide to do it, and I believe it's the continuation of the struggle." This doesn't mean group meetings are always easy, or that everybody always agrees, but they want the same outcome. A lot of their work is in education: Faraj and other Palestinian members go with their Israeli colleagues to speak in schools, reaching 25,000 students every year.

"When I was young, all I knew of Israelis was the soldier or the settler, but something happened to change that picture. I met Rami Elhanan [another prominent Parents Circle member], an Israeli from Jerusalem who lost his daughter in a suicide bomb attack. He talked about his suffering and pain, and I found a new picture of the Israeli side, which is the human side. It doesn't mean I'm falling in love with the Israelis or I forget what has happened in my life, but I have a new picture now."

Each has faced some hostility from their own communities for the work they do and there are many times when their own commitment to reconciliation is tested. Damelin remembers hearing reports – mistaken, it later turned out – that the man who killed her son was one of the hundreds of Palestinian prisoners who would be released in exchange for the safe return of the captured Israeli soldier Gilad Shalit.

Even though she has supported prisoner releases to ease negotiations, "that was really a test. It's easy to talk about reconciliation and peace and it all trips off your tongue, but do you mean it? Sometimes it's very hard. You become very defensive about your own people. I love Israel. It's not that I have become a Palestinian. I just think that the occupation is killing the moral fibre of my country and for that I will fight."

Damelin and Faraj both travel a lot, giving talks, meeting politicians and other groups. I ask what kind of picture she gets of how the conflict is viewed from outside and Damelin sighs: "This whole idea of being pro-Israel or pro-Palestine – what comes out of that is that you are not helping either nation and you are importing our conflict into your country. That is very clear in Britain. If you are pro-Israel or pro-Palestine, and your leaders are encouraging this – some of your politicians, it is very clear whose side they are on – the Jews and Muslims here are beginning to hate each other. It's very easy for both the Muslim and Jewish communities in the diaspora not to compromise; they're not exactly put to the test every day. If you can't be part of the solution, I would really ask you to leave us alone. I really mean that."

Damelin grew up in South Africa. Her recent return to the country was made into a film, One Day After Peace, in which she talked to people about South Africa's Truth and Reconciliation Commission and what could be learned from it. "The most amazing thing is that it's such an affirmation of the work we're doing now," she says.

In South Africa she was an anti-apartheid campaigner but left in 1967, not quite believing apartheid would end: "I believe that a miracle happened in South Africa and I think a miracle could happen for us too. I have hope. We can't afford to give up hope."