Blair represents the UN, US, EU and Russia in his role as Quartet Middle East envoy - a job he was given after leaving Downing Street in 2007. The former prime minister discussed the Palestinian economy as well as the Middle East peace talks with Cameron.
The pair also discussed Blair's Palestinian economic initiative, which aims to promote growth in the West Bank and Gaza Strip.
After the meeting, the former Labour prime minister gave his backing to Cameron's drive to boost economic links.
Blair said: "The British Government has actually got a great opportunity here, because it is relatively trusted by both sides, which is quite rare in this situation.
"I think we have got the right idea on relationships between a political negotiation to resolve all the difficult issues about borders and security and Jerusalem and so on, and the economic side, which is absolutely vital because if we don't build the Palestinian economy up at the same time as you are pursuing the political negotiation then a state for the Palestinians seems a dream and not a reality."
Asked whether yesterday's missile attack could knock the peace process off track, Blair said: "The strikes from Gaza just underline and illustrate the depth of the problem. Gaza continues to be under lockdown, with extremist groups operating and the people in a desperate situation."
He added: "However, I don't think, even with these rocket attacks, that should get in the way of pursuing a political process and a political negotiation that allows, under the leadership of the US, the two sides to come together and to try and describe an outline of what the two-state solution looks like and how a Palestinian state is going to be and to operate and to function."
Cameron will meet with Abbas later today, in an attempt to bolster efforts to rekindle the stalled peace process. On Wednesday he met with Israeli prime minister, Binyamin Netanyahu.
Yesterday Cameron echoed the words of US secretary of state John Kerry when he appeared to recognise Israel as "the nation state of the Jewish people", long a bone of contention for the Palestinians in any peace deal.
In a speech to Israel's parliament, the Knesset, on his first visit to the country as prime minister, Cameron urged Israel to pursue a peace deal with Palestinians that could mean "an end of all conflict" in the Middle East.
"Imagine what this land would be like if a two state solution was actually achieved," he said. "On Israel's relationships, imagine, as John Kerry put it: "mutual recognition of the nation state of the Palestinian people and the nation state of the Jewish people.
"This is about justice for two peoples. Dignity for the Jewish people and yes, dignity for the Palestinian people too."
The words in Cameron's speech appear to technically go further than the Foreign Office line, which has always been that a state needs to be defined by its borders, first and foremost.