Mr Barghouti, the general secretary of Fatah, the largest Palestinian political movement in the West Bank, told The Independent: "You can expect in the next few weeks a wave of suicide bombs in Israel."
He said it was almost inevitable that Hamas, whose suicide bombs killed 58 people earlier this year, would carry out more suicide attacks in order "to get the support of the people" by capitalising on Palestinian anger.
Mr Barghouti was speaking close to the scene of some of the heaviest fighting between Israeli troops and Palestinian police on Thursday. As he explained why he thought the violence was going to get worse, several hundred Palestinian young men, about 100 yards away, were trying to storm a house held by Israeli soldiers by hurling Molotov cocktails. The troops replied with rubber bullets. At one moment, part of the hillside caught fire, sending up plumes of smoke.
Protected by a wall from the rubber bullets which crashed into the windows of an office block overhead, Mr Barghouti said he thought the closure by Israel of the tunnel running under the Muslim quarter in Jerusalem would no longer be enough to end the armed clashes. He said: "The Israeli government will have to implement the peace process by pulling out of Hebron, continuing the redeployment of its troops on the West Bank and releasing our prisoners."
Mr Barghouti said the instructions to Fatah activists were to continue the demonstration.
Asked if it was possible that Benjamin Netanyahnu, the Israeli Prime Minister, would order his army to take over Ramallah or the other automonous Palestinian towns, Mr Barghouti said the whole situation in the West Bank and Gaza had changed since 1994: "When the Israelis left we had hundreds of weapons. Now we have thousands."
Even if the Israelis had tanks and helicopters they would suffer serious losses, something underlined by the deaths of 13 soldiers this week, he said. As Mr Barghouti spoke, the bizarre position of the Palestinian police in Ramallah was emphasised when they tried to stop the young men from attacking the Israeli-occupied area.
The police had themselves been fighting the Israelis at the very same spot the previous day - the back window of a blue police van had the picture of a policeman who was killed, with the heading "a martyr in the battle of Jerusalem"over it - and the rioters did not welcome their intervention. They turned on the Palestinian riot police, equipped with see-through plastic shields and hurled volleys of stones, forcing them to retreat. In one sense, both sides were within their rights. The Palestinian rioters, hurling stones and mineral water bottles filled with petrol, were holding a hill which is in autonomous Ramallah. The house they were trying to set on fire was just outside the town in so-called area "B", where the Israelis control security. Neither side was using live ammunition, although there were several hundred Palestinian police - many wearing combat uniform - carrying sub-machineguns standing nearby. Mr Barghouti was clear about the rules of engagement: "If the Israelis come over the hill or fire live rounds then the police here will shoot back."
Mr Barghouti and the Palestinian leadership do not appear dismayed by events. By opening up the tunnel, Mr Netanyahu has forced Palestinians to rally around Mr Arafat, whose popularity has waned because of the failure of the Oslo accord to better the lives of Palestinians and the brutality of the police and security forces.
The Israeli tunnel and the threat to the Muslim holy places is also an issue likely to maximise support for Palestinians in the rest of the Arab world. "It is a much better issue for us than the increase in Israeli settlements on the West Bank," one Palestinian analyst said.
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