Newly-appointed Middle East envoy Tony Blair has said he is optimistic that momentum can be regained in the stalled Israeli-Palestinian peace process.
Mr Blair is expected to travel to the region next week
Attending his first meeting of the Quartet group in Lisbon, he said there was "no more important issue for peace and security in the world".
It was the group's first meeting since the Islamic militant group Hamas seized control of the Gaza Strip last month.
The Quartet is made up of the EU, the US, Russia and the UN.
The representatives were US Secretary of State Condoleezza Rice, her Russian counterpart Sergei Lavrov, UN Secretary General Ban Ki-moon and EU foreign policy chief Javier Solana.
Addressing a news conference after the meeting, Mr Blair said: "There is a sense that we can regain momentum. That is the crucial thing.
"If we are able to regain that momentum then a whole lot of things become possible, not least the fact that those people of peace can then feel that the force is with them, and not with those who want conflict."
He said it was important to work towards a two-state solution to the Israeli-Palestinian problem - with Israel confident of its security, and a Palestine with viable institutions.
The former British prime minister said he was an optimist, and would probably need that quality in the months ahead.
Mr Blair is expected to travel to the region next week, where he said he planned to "listen, to absorb and to reflect" before putting forward any proposals.
Mr Blair's mandate is limited to helping the Palestinians to develop their institutions and economy.
Hamas received fresh criticism from Ms Rice and Mr Amado
But if Mr Blair wants to be more than a fringe player in the Middle East, says the BBC's Middle East editor Jeremy Bowen, he will have to get Israel, the Palestinians and the Quartet members talking about final status issues.
These include the position of Israel's permanent borders, Jewish settlements on Palestinian territory and the fate of Palestinian refugees.
There is also the status of Jerusalem, claimed by Israel as its capital, but where the Palestinians also want to make their capital.
Hamas out in the cold
Mr Blair's appointment last month was welcomed by Israel and the Palestinian Authority, led by Mr Abbas, whose Fatah faction controls the West Bank.
However, Hamas said Mr Blair had not been honest or helpful while prime minister, because of his position during Israel's war against Hezbollah in Lebanon and the invasion of Iraq.
Hamas took full control of the Gaza Strip by force last month
The Quartet wants Hamas to recognise Israel's right to exist, renounce terrorism and sign up to past agreements with Israel.
Before the meeting, Ms Rice and Portuguese Foreign Minister Luis Amado, whose country holds the rotating EU presidency, rejected dealing with Hamas until it recognised Israel.
"We have a very good partner in Mahmoud Abbas... It makes very good sense to work with him, and Hamas, I think, knows what is expected for international respectability," Ms Rice said.