"Mr Blair is the most qualified person on earth to resolve this issue"
Dave, London, UK
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Blair said he was an optimist and played on his success in Northern Ireland, saying that 10 years previously people would have been "completely unbelieving" that the two factions would have "sat down in government together".
Blair, who was prime minister of Britain for 10 years, is widely credited with the success of the Northern Ireland peace process.
But Sharif Hikmit Nashashibi, chairman of Arab Media Watch, speaking to Al Jazeera, said Blair had offered only "five minutes of fluff and generalisations".
"There was no real meat to what he was saying," he said. "It's typical Blair."
He said the Quartet itself had done "next to nothing" to work towards a solution.
"They talk a lot, they come out with generalisations, they portray the conflict as one of two equal sides but on the ground they have achieved next to nothing. And they've appointed an envoy that will continue that level of success."
At a press conference before the meeting in Lisbon, the Portuguese capital, the US and EU confirmed their refusal to deal with Hamas.
Both Rice and Luis Amado, the Portuguese foreign minister whose country currently holds the rotating EU presidency, rejected dealing with Hamas, even as critics questioned whether the stance could compromise Blair's work with the Palestinians.
Rice said: "Hamas, I think, knows what is expected for international respectability."
Speaking for the EU, Amado said: "I see no conditions at the moment to engage [in] new relations with Hamas without a new position from them."
Hamas took control of the Gaza Strip in June, forcing out the Fatah faction led by Mahmoud Abbas, the Palestinian president, which is now concentrated in the West Bank.
The split in the Palestinian leadership has placed another obstacle in the way of a peace deal, but it has also prompted Israel and the West to seek ways to support Abbas, whose West Bank-based government is the only one recognised by the Quartet.