Tony Blair has said he believes a peace settlement between the Israelis and Palestinians is achievable.
Mr Blair is Middle East envoy for the US, Russia, the UN and the EU
The former PM, who acts as Middle East Quartet envoy, said he was "cautiously optimistic" that a deal could be struck by the end of the year.
Mr Blair spoke after a meeting in Jerusalem with US President George W Bush, who is on a Middle East tour.
Mr Bush has called on Israel to end its occupation of some Arab land to allow the creation of a Palestinian state.
He was speaking in Jerusalem following two days of separate talks with Israeli and Palestinian leaders.
It is thought to be his strongest public statement pressing Israel to give up land it seized in the 1967 war.
The US president has repeatedly said he believes a peace agreement can be reached by the end of the year, and says he wants a peace deal signed by the time he leaves office in January 2009.
In a television interview, Mr Blair was asked if he agreed with Mr Bush that a peace deal was achievable.
"Sure, it is absolutely possible to have a peace deal by the end of the year if people want to make it happen," he said.
But to achieve this, those involved had to be prepared "to have the courage to take the difficult decisions to make the difficult compromises", he said.
He also said people underestimated the determination of Mr Bush and US Secretary of State Condoleezza Rice, who he described as "absolutely and totally committed" to finding a solution.
"I think given the determination there is to succeed and given the desire on the part of the American leadership, the Israeli leadership, the Palestinian leadership to see it happen, I think people could be surprised this year."
'Nothing more important'
Mr Blair, as envoy for the Quartet - the US, Russia, the UN and the EU - has spent much of the last few months on the ground in the Middle East trying to work out how to help the Palestinians build better institutions - the foundations for a future Palestinian state.
There was "no option" but to have both a state of Israel and a state of Palestine "living side by side", he said.
He added that in the longer-term most "sensible Israelis" knew the only real solution to security problems was a peace deal with the Palestinians.
"People in Israel - they don't want to pay the price of the world's desire to have a peace deal, and I totally understand that and I am a strong supporter of the state of Israel, and this should only happen under terms which guarantee Israel's security.
"But if we can achieve those terms and give the Palestinian people a state, then I think there is nothing more important in the battle against... extremism and terrorism that is fairly deep-rooted in many parts of the world today."
Palestinian leader Mahmoud Abbas and Mr Olmert vowed at a US summit in Annapolis last year to try to achieve a two-state solution by the end of 2008.
On Tuesday, the two leaders said negotiations could begin on the core issues separating them such as the borders of a future Palestinian state, Palestinian refugees, Israeli settlements and the status of Jerusalem.
It was crucial for talks not to lose momentum, Mr Blair said, but he was "cautiously optimistic" about reaching a settlement.
"There is no alternative but to push forward and to do so with determination," he added.