Tony Blair believes Israel and the Palestinians have "no alternative" other than a return to peace negotiations.
The Quartet's Middle East envoy said the growth of the Palestinian economy, coupled with improved security for Israel and a resolution to the current political stalemate, could realistically bring a successful conclusion to the peace process.
Mr Blair said: "What President Obama is trying to say at the moment is that we need to give this a direction and a shape and he is also, I think, worried about the situation Israel is in, if it doesn't realise it has to have a position on peace. What mustn't be in doubt is that people want peace."
The former Prime Minister was speaking last Thursday at a London event organised by UK Israel Business, the Portland Trust and the Palestine Britain Business Council, in central London.
Mr Blair said successes on the ground in recent months should encourage those working for peace.
He said: "What we are trying to do is very much based on Palestinian institution building, the economy and security. Although the politics has ended up in its present impasse, actually there has been real change on the West Bank and even in the last few months in Gaza.
"The majority of people in this situation just want to get on with their lives. They want a decent standard of life and I believe very strongly in relation to Gaza that the easing [of the blockade] we have seen in the last six months has actually played a part in undermining the popularity of Hamas there, and we have to keep that going."
A year after the Gaza flotilla incident in which nine Turkish activists were killed, Mr Blair said he backed Israel's actions to defend itself: "I am completely supportive of Israel when it comes to checking boats or anything else that wants to come into Gaza. Israel has a complete right to protect its security.
"But where it's about things coming into or indeed out of Gaza which have no security implications it's really sensible to support the local population."
But he admitted: "There is no belief at the moment that either side will come to this negotiation in good faith. The challenge is to keep going."
Portland Trust chairman Sir Ronald Cohen said continued improvement of the Palestinian economy was essential.
Sir Ronald said: "If you look at the links between extremist views and economic conditions, it seems to me that there is no doubt that poverty breeds extremist ideology.
"The perception that there isn't a partner for peace on the other side is constantly reinforced by extremist groups on both sides."