Standing alongside Mr Blair, Palestinian President Mahmoud Abbas said he was prepared to sit down with the Israeli Prime Minister Ehud Olmert.
"We are ready immediately for serious negotiations to end the conflict," Mr Abbas said. "I am ready to meet Prime Minister Ehud Olmert without conditions."
While no date has been set, Israel says it will work to bring about the meeting soon.
Mr Blair, who is credited with prodding the two leaders into the agreement, also attempted to draw Hamas into the peace efforts but the group, which controls the Palestinian government, rejected the condition that it must first renounce violence and recognise Israel.
Bleak opportunity
"For the past months, the situation has gone backwards and not forwards," Mr Blair said at a joint news conference with Palestinian President Mahmoud Abbas.
Now, he added, "there is window of opportunity, even if it does seem very bleak."
Mr Olmert and Mr Abbas were on the verge of holding their first working meeting in June when Palestinian militants kidnapped an Israeli soldier. That action derailed the meeting and sparked a broad Israeli offensive into the Gaza Strip.
Mr Olmert had insisted that there could be no talks before the release of the captive solider, who is still being held by militants, while Mr Abbas demanded an Israeli commitment to release Palestinian prisoners.
But in talks with his British counterpart, Mr Olmert dropped his demands and declared that he was ready to meet the Palestinian leader without conditions. He had been calling publicly for talks with Mr Abbas last week, after shelving plans for a large scale pullback from parts of the West Bank.
Agenda
Both sides declined to say when the meeting between the two leaders would take place, or what would be on the agenda.
Israel is likely to push for the release of the kidnapped soldier, while the Palestinians could seek help in easing the tough economic restrictions on the Gaza Strip and urge Mr Olmert to free some of the thousands of Palestinian prisoners being held by Israel.
"It must be a real working meeting, but we should not expand expectations," Palestinian lawmaker Saeb Erekat said.
Mr Olmert's spokeswoman, Miri Eisin, said Israel is interested in bolstering Mr Abbas, who is locked in a power struggle with Hamas, the group democratically elected earlier this year.
"It's important to show support for moderate voices in the Palestinian community," she said.
Ms Eisin ruled out a prisoner release until the kidnapped Israeli soldier returns home, but did say Israel is prepared to take unspecified “creative” actions that go beyond humanitarian gestures.
But Israel’s Foreign Minister Tzipi Livni says talks based on the internationally backed “road-map” will not be conducted until Hamas renounces violence.
"In the first stage (of the plan), there is a cessation of war and the disarming of terror groups," she told Israeli television.
Unity government
Mr Abbas has been urging Hamas to join him in a "unity" government. He headed to Gaza to begin a new round of talks with the group, in the hope that a coalition will force Hamas to soften its ideology and help lift painful economic sanctions.
Mr Blair welcomed those efforts saying the world should fully restore contacts with the Palestinians if Hamas agrees to a unity government.
But he added that a coalition would have to accept conditions set by the international sponsors of the "road map" - renouncing violence, the recognition of Israel and acceptance of previous peace agreements. It has made little progress since being launched three years ago.
Hamas spokesman Sami Abu Zuhri said the group was ready to form a government with Fatah, but "not according to standards that are dictated".
"We are doing everything possible to lift the siege against the Palestinian people but this will not be done at the expense of Palestinian principles and rights," Mr Abu Zuhri said.
"Hamas supports the creation of a national unity government, put in place for the Palestinian people and not for powers abroad," he added.
Desperate situation
Meanwhile, the United Nations Relief and Works Agency for Palestinian refugees has increased the amount of food aid to refugees in the Gaza Strip because of the “desperate” situation there.
"In response to an unprecedented situation in Gaza, UNRWA has increased the amount of the food distributed for the first time in five years," said John Ging, who heads the agency in the Gaza Strip.
Mr Ging said that beginning Wednesday, 1,000 tons of additional food aid would be distributed to thousands of refugee families ahead of the Muslim holy month of Ramadan, which is due to start mid September.
Some 830,000 people, or 60 percent of the Gaza Strip’s population receives UN aid.
"It is not acceptable that this situation continues," Mr Ging added.