Hamas has been isolated because of its refusal to meet three criteria: recognition of Israel's right to exist, renunciation of violence and adherence to interim peace deals with Israel.
Michael Gapes, chairman of the committee, said the the world's lack of a positive response had contributed to the deteriorating situation.
He told al Jazeera: "We believe that now there is absolute necessity to get back to establishing a unity governement amongst the Palestinians again.
"And you can't get a Palestinian state and a two state solution unless you include Gaza as well as the West Bank.
"That means engaging with moderate elements within Hamas in order to try to facilitate political compromise and move Hamas towards the process set out by the Quartet including its principles of non-violence, recognition of Israel, and abiding by all previous agreements."
Fighting between Hamas and the rival Fatah movement eventually led to Hamas taking control of the Gaza Strip in June, while Fatah - the faction led by Mahmoud Abbas, the Palestinian president - administered the West Bank.
The committee also criticises Blair for not calling for an immediate end to the war between Israel and Lebanon's Hezbollah movement last summer, concluding that his failure to speak out damaged Britain's reputation and led to high casualties among civilians.
The report also said that Washington's so-called "surge" tactic in Iraq was likely to fail. It called on the British government to help Iraqi factions reach agreement on key issues.
Gapes said: "I think it's important to recognise that whereas the US has been carrying out an increase in its military presence with 30, 000 additional troops under the 'Surge', the British presence has been reduced down to around 5, 000 and will go further down over coming months.
"The question is 'how long will it take for Britain to completely withdraw?' But we're not saying we should set arbitrary timetables.
"What we are saying is the real answers to the problems in iraq is going to be an internal accommodation on questions like the constitution, the allocation of oil revenue, the process of de-Baathification, those issues have to be resolved internally by the Iraqi politicians although we think that the coalition and the UN could give assistance to that process."