Israeli Prime Minister Ehud Olmert has said he is ready to begin talks with Palestinian leader Mahmoud Abbas to advance peace efforts.
Mr Olmert said the meeting was not conditional on the release of the Israeli soldier, Cpl Gilad Shalit, held by Palestinian militants.
But he said the soldier's release would be at the top of the agenda.
His remarks came after a meeting with UK Prime Minister Tony Blair, who is seeking to revive the peace process.
Mr Blair said the stability of the Middle East was essential to the rest of the world, including the UK.
On the recent Lebanon conflict, Mr Blair said he wanted to work to make sure the UN resolution that ended the conflict was fully implemented.
BBC diplomatic correspondent Jonathan Marcus says Mr Blair is intent on a world role despite acknowledging his imminent retirement from office.
Mr Olmert last met Mr Abbas in Jordan in June, but soon afterwards Cpl Shalit was captured by Palestinian militants in a cross-border raid from Gaza.
Since then more than 200 Palestinians have been killed in Israeli raids and strikes on Gaza, and the territory's borders have been largely sealed.
The BBC's James Reynolds in Jerusalem says Mr Blair can claim Mr Olmert's offer to speak to Mr Abbas as a very small step towards peace.
"I intend to meet with chairman Abbas in order to make progress on outstanding issues on our agenda," Mr Olmert said.
"I have no preconditions or prerequisites for such a meeting."
Mr Olmert and Mr Blair talked a lot about the importance of the Middle East peace plan, the road map, which has been largely neglected for three years.
The British prime minister admitted that the plan was still at a very preliminary stage.
Closeness to US
The two leaders also discussed the fragile ceasefire between Israel and Hezbollah.
Mr Blair said he thought that, although the Middle East was at a difficult point in its history, peace could still be achieved with goodwill and the right leadership.
The UN resolution on the Lebanon ceasefire could contribute to this, he said.
"If 1701 is implemented fully then this will be a major strategic advance for peace in the region," he said.
"We will do everything we can so that the resolution is implemented."
Our correspondent says there is a certain irony about the visit, in that it is his closeness on policy towards the region to the Bush administration which in many ways has undermined his position at home.
But Mr Blair defended his friendship with the US, saying it was not a mistake to stand shoulder to shoulder with Washington after the 11 September 2001 attacks.