US President Mr Bush said today the death of Yasser Arafat was a "significant moment in Palestinian history".
His statement said: "We express our condolences to the Palestinian people. For the Palestinian people, we hope that the future will bring peace and the fulfillment of their aspirations for an independent, democratic Palestine that is at peace with its neighbours."
French President Mr Jacques Chirac, who visited the dying Arafat in hospital last week, called him "a man of courage and conviction".
British Prime Minister Mr Tony Blair, who has made Middle East peace a cornerstone of his foreign policy, said: "The most important thing is to make sure we reinvigorate the peace process because there is misery for Palestinians, there is misery for Israelis who suffer terrorist activity."
British Foreign Secretary Mr Jack Straw said he would attend Mr Arafat's funeral on behalf of the British Government.
He expressed "deepest sympathy and condolences for the death of President Arafat.
"He was a towering figure not only in the Palestinian world but in the Arab world and it is difficult to imagine the Middle East without him," Mr Straw said.
Israeli Prime Minister Mr Ariel Sharon told reporters: "The latest events are likely to present a historic turning point in the Middle East."
He said progress towards peace required Palestinian leaders to "wage a war on terror".
Israel's Mr Shimon Peres, who shared the Nobel prize with Mr Arafat and slain Israeli leader Yitzhak Rabin in 1994, told Israel Radio: "Arafat's biggest mistake was when he turned to terrorism. His greatest achievements were when he tried to turn to peace."
Israeli President Mr Moshe Katsav said in a statement: "I hope the Palestinian leadership will start a new direction that will put an end to the violence and the terror against Israel and will allow us to re-engage in negotiations for a possible agreement between us."
Israeli justice minister Mr Yosef Lapid blamed Mr Arafat for global terrorism and the failure to achieve Middle East peace, but he expressed hope of improved relations under new leadership.
"I hated him for the deaths of Israelis. . . . I hated him for not allowing the peace process . . . to move forward," Mr Lapid told Israel Radio.
UN Secretary General Kofi Annan said this morning he was saddened by Yasser Arafat's death.
He said Mr Arafat was "one of those few leaders who could be instantly recognised by people in any walk of life all around the world."
"For nearly four decades, he expressed and symbolised in his person the national aspirations of the Palestinian people."
The Vatican praised him as a charismatic leader who struggled to win independence for his people, and repeated its support for a sovereign Palestinian state alongside Israel.
A Vatican statement called Mr Arafat the "illustrious deceased" and asked God to grant eternal rest to his soul.
South African President Mr Thabo Mbeki said history would record that Arafat had given hope to millions "by instilling in them the knowledge and consciousness that despite current difficulties, they hold the gift of freedom in their hands".
But Australian Prime Minister Mr John Howard said: "I think history will judge him very harshly for not having seized the opportunity in the year 2000 to embrace the offer that was very courageously made by the then Israeli Prime Minister Ehud Barak."