In a poky office less than a ten-minute walk from Downing Street, Tony Blair looks like a man reborn. Gone is the haggard look of his final days as Prime Minister, replaced by a rejuvenated figure who has reinvented himself as a global diplomat with a mission.

The job might sound seductive for a retired leader or elder statesman looking for a new role to play on the world stage but few would envy Mr Blair’s job description as co-ordinator for the Middle East Quartet. This unhappy group, representing America, Russia, the United Nations and the European Union, has been trying and failing for years to reach the Holy Grail of international diplomacy: a peaceful solution to the seemingly endless ArabIsraeli conflict.

The issue has already consumed years of peace talks, defeated some of the finest diplomatic brains and at its lowest points cost the lives of thousands of Israelis and Palestinians, mostly civilians.

Now the seemingly impossible task has landed at Mr Blair’s feet. He and President Bush have pledged to try to solve the conflict by the end of this year, when it is hoped that a Palestinian state can be declared, existing peacefully alongside Israel.

So why choose Mr Blair? He certainly does not need the unpaid job. He has already signed up as a consultant to JP Morgan and Zurich Financial Services. He is writing his memoirs, has launched a sports academy in the Northeast and later this year plans to open a faith foundation.

In his decade in office the Middle East probably inflicted more harm on his leadership than any other region. He was fatally wounded by the military campaign in Iraq. He was damaged by the failure to deliver progress on Middle East peace. His support for America and Israel in the war in Lebanon in 2006 hastened his removal from office.

Yesterday these setbacks were consigned to history. Mr Blair made clear that he was focused firmly on the future. “I am absolutely passionate about this,” he told The Times. “I believe that the Middle East is a region in transition. The question is transition to where? It can go to one of two places. One is where the economy becomes the cutting edge of globalisation so the politics and culture and forces for moderation and modernisation win out.

“Alternatively, it becomes a region dominated by a particular and exclusive and wrong-headed view of Islam and a major threat. Resolving the Arab-Israeli issue would give an enormous boost to the forces of moderation. Resolving it would be a hugely symbolic act, not just between Israel and Palestine but Islam and the West between people of different faiths. There is nothing more important to world peace than resolving this question,” he said.

Few would question the benefit of a deal for the Middle East and the cause of peace throughout the world, but there is deep and well-founded scepticism that it can be achieved any time soon, certainly not in the last 11 months of Mr Bush’s presidency.

In typically rosy and robust fashion, Mr Blair tries to dispel the doubts the moment you set foot in his tiny office in St James’s, where staff are squashed on top of one another, waiting for new offices to be renovated in Mayfair. “This is a deal that could definitely be done, and it could definitely be done this year,” he said, between his monthly visits to Jerusalem, devoted to prodding and pushing the process forward.

To his advantage, none of the main players in the region challenges the basic concept of a two-state solution, but few could plot a course that would lead there. As one Israeli commentator put it: “There is light at the end of the tunnel, it is just that there is no tunnel.”

The first significant obstacle is the weak and divided Palestinian Authority. The Authority may rule over parts of the West Bank but it no longer carries authority in the Gaza Strip, where the militant group Hamas is firmly in control.

Mr Blair believes that the current strategy towards Gaza, which was until recently blockaded by Israel as punishment for Hamas rockets that had been fired at Israeli civilians, is badly flawed. “Hamas have a clever strategy, which is why I keep saying we need a clever strategy as well, which helps the people, isolates the extremists and points out the fact that if at any point in time the rockets stop, the whole situation will be transformed,” he said.

The former Prime Minister might not have armies or officials at his disposal any more, but he has accumulated an impressive war chest of $7.7 billion (£3.8 billion) to be spent on reconstruction in Palestinian areas and invigorating the economy.

The money could be a potent weapon to use against Hamas, but only if Israel allows him to spend it on projects and is prepared to lift the siege of Gaza. The same is true for the West Bank, where Mr Blair insists that the local economy is showing signs of recovery but where Israel’s tight security controls restrict travel and trade.

Even a few months ago the local geography of Palestinian areas might have been a mystery to Mr Blair. Not any more. Now he is familiar with Japanese projects in Jericho, housing plans for Ramallah, industrial parks in Jenin and a water treatment plant for Gaza. With a suite of offices at the famous American Colony hotel in Jerusalem, he can even claim to be a resident of the world’s religious capital.

Much of what happens next to Mr Blair will depend on his relationship with the Israelis, who will be asked to make the concessions on security to help the Palestinians. “My relationship with the Israelis is good,” he said. “I genuinely admire what they are trying to do. One thing I do do, and I get criticised for it, is to state the Israeli point of view from time to time.”

His interlocutor is Ehud Olmert, the Israeli Prime Minister, who is clinging to power. His ruling coalition Government is starting to falter, he narrowly avoided being dethroned this week by an official report into the disastrous Lebanon war of 2006. He remains vulnerable and unpopular.

Nevertheless, if Mr Blair is to succeed he needs Mr Olmert to remain firmly in place and strong enough to make concessions to the Palestinians.

Mr Blair said that he had tried to adapt his experiences from Northern Ireland peacemaking to the Middle East but he had learnt that the character of the two conflicts was very different. In particular, he believes that unless confidence can be returned to the relationship between Israelis and Palestinians the chances of reaching a deal are slim.

“The question is how do you create the circumstances on the ground where the Israelis get confidence that their security concerns are being met and the Palestinians get confidence that the occupation will eventually be lifted,” he said.

“Without that confidence about the state of the situation on the ground the negotiation becomes more difficult. Sometimes people have looked at this process as one in which if you cut the deal the facts on the ground will alter. In my view it is as much the other way around. Unless you can change the facts on the ground the deal becomes difficult to cut.”

Finally, the former Prime Minister needs to keep faith in Mr Bush, who has repeatedly promised but consistently failed to provide serious American diplomatic muscle to deliver a peace deal.

Last year the Bush Administration hosted a Middle East peace conference in Annapolis, where the ambitious goal for Palestinian statehood was set out. Mr Bush followed up the initiative with a visit to Israel and the West Bank last month and a promise to return later this year.

Mr Blair insisted that he was confident that his old ally was serious this time about delivering a result, even as his power ebbed away.

“I am unworried by the fact that it is President Bush’s last year in office,” he said. “Firstly, President Bush is immensely popular in Israel. Secondly, I did the Northern Ireland deal the month before I left.

“The American engagement in this has altered significantly both in quality and quantity in the past two months, there is no doubt about that. When I saw him [Bush] in Jerusalem, he was completely up for it.”

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