One day in November 2000, Natalia Wieseltier tried to telephone a friend from her home in Tel Aviv. She dialled the wrong number - but it was the best mistake she has ever made. The call went through to a Palestinian man living in Gaza. The intifada had just started and relations between Israelis and Palestinians were at their lowest point in years. But the man spoke some Hebrew, and instead of hanging up he and Wieseltier started to talk.

"I asked him how he was and he said, 'We're afraid - there's a curfew and there's no one on the streets; my wife is having a baby and we can't get to the hospital.' Then he said he was surprised a Jew talked like this. I was saying nothing special, I was just talking. I left him my number, and the next day he left a message on my answer machine."

She called him back, and he passed the phone to his brother and his uncle and Wieseltier spoke to them, too. They handed on her number to friends in Ramallah and Jenin. "I realised it was something magic, just talking to these people like this. It was so direct. Then I realised that they all probably thought there was only one freak in Tel Aviv who would speak to them." So she gave their phone numbers to her friends.

The result, two years on, is one of the most remarkable stories of hope and reconciliation to emerge from the Middle East conflict. Wieseltier and a friend, Shmulik Cohen, met with Yitzhak Frankenthal, an Orthodox Jew whose son was killed by Hamas in 1994 and who has become a leading peace campaigner. Frankenthal heads the Families Forum, which promotes dialogue between Israeli and Palestinian families that have lost a relative in the fighting. Together, he, Wieseltier and Cohen set up something even more ambitious: a telephone hotline that Palestinians and Israelis can use to speak with someone on the other side.

Billed as "Hello, Salaam! Hello, Shalom!", the hotline was launched last October with two weeks of radio, billboard and newspaper advertising. So far, more than 80,000 people have called the line from across Israel and the Palestinian territories, people living everywhere from refugee camps to affluent suburbs. In total, they have talked for more than 300,000 minutes. In the current climate of fear and mistrust, when moderates on both sides hardly have a political voice, this success seems astonishing.

Cohen, who now manages the project, is not surprised. "I thought there was a need for it. I believed Palestinians and Israelis wanted to talk to each other as human beings."

To use the system, you call *6364 from either side and you are put through to an automated answer system: "Press 1 if you wish to talk to an Israeli, 2 if you want to talk to a Palestinian." You are asked if you would like to speak to someone on the other side and if you want to open your own box so that others can speak to you, and then if you would rather speak to a man or a woman, or to someone of a particular age group. A computer searches the database and patches you through. After that it's up to you - you can talk, end the call and leave it at that, or you can exchange numbers and carry on a relationship beyond the Hello, Shalom! system. Thousands of people have done so.

One of them is Nadim Asmar, a Palestinian student from outside Bethany who heard about Hello, Shalom! on the radio. He has telephoned seven Israelis, four of whom he has exchanged numbers with. "I had been wanting to talk with Israelis but I didn't know how," he says. "Israelis and Palestinians have become increasingly separated over the past few months. We've become very far away from each other."

Making the first call can take considerable courage. "I tell you, my hand was shaking," says Asmar. "I was thinking, what will they say to me? Will they call me a terrorist? But they didn't. In fact they were very nice." It has, he says, transformed his views of Israeli people. "I thought they were selfish, that they didn't understand what was going on here or didn't want to know. But I was wrong. Like us, they want to live, they want to travel without fear of being blown up . . . First of all, they're human beings."

This illustrates how Hello, Shalom! has, as Cohen puts it, "absolutely changed people's perceptions of the other side". He recalls a student at a school in Israel telling him how he had persuaded his grandmother, a staunch right-winger, to call Hello, Shalom! At first she had scorned the idea, but when she finally made the call she came off the phone amazed at what she'd heard. "They're just like us," she exclaimed.

Because of the hardline politics and the mutual suspicion on both sides, talking with "the enemy" can be frowned upon, especially in the Palestinian territories, where the price of being a suspected collaborator is a bullet in the back of the head. Asmar says he got a mixed reaction when he told his friends and work colleagues that he had spoken with Israelis. Some asked him what they were like; some dismissed the idea, saying that Israelis would never respect them; and others accused him of collaborating.

The success of Hello, Shalom! reflects what peace activists claim is a resurgence in grass-roots contact between Palestinians and Israelis, many of whom have become disenchanted with their political leaders and their failure to achieve peace. Frankenthal says people are beginning to understand that the detachment between the two societies is "enabling Sharon and Arafat to persist with their war games, based on the hatred and fear that people have developed for each other". He has taken advantage of this resurgence and has managed to convince Arafat, as well as several senior Israeli political and military figures, to put their names to a draft "ceasefire" agreement, as the first step towards peace. His plan is to get 250 officials on each side to sign the declaration in Jerusalem, and to get Tony Blair to witness it as international mediator. Downing Street is apparently "considering" the proposal. "This is not a political thing, it's coming from the grass roots," Frankenthal says. "We're saying, enough is enough."

Meanwhile, the idea is to get ordinary people talking to each other. Wieseltier, who has already made more than 280 calls to Palestinians, thinks that people are desperate for peace. "It's a matter of do it or die. There's no other way for each of us to go."

A few cynics have asked what point there is in talking if you can't meet. But the beauty of talking, says the Hello, Shalom! team, is that it forces you to recognise the humanness of the other person. "Sometimes when I am talking to an Israeli now," says Asmar, "I feel I am talking to a Palestinian."