The former British prime minister's associates have said that the coming weeks will be critical and will be make or break for the chances of an agreement.
In an interview with the Sky News network during a visit to the West Bank city of Jenin, Blair called on Israel to remove roadblocks and lift restrictions on the Palestinians in a bid to improve their economy.
The Quartet has asked Israel to dismantle 12 roadblocks across the West Bank, but only one has been removed so far.
"There are a whole set of proposals that we've put to the Israelis and actually the next few weeks will be critical on delivering those and yes, removing one is not enough. But what is necessary is for Palestinians to be able to move relatively freely around their own territory. That is what they cannot do now," the former British prime minister said.
According to Sky News, Blair was mobbed by hundreds of Palestinians when he went on walkabout through Jenin's marketplace, potentially a nightmare for his security detail but one that passed without incident.
Blair believes the Palestinians are making progress and so are countries supporting them with money - and there are signs the Israelis are seeing how they can help, he told Sky.