UK Prime Minister Tony Blair has met his Israeli counterpart at the start of a weekend visit to the Middle East.
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.
Israeli Prime Minister Ehud Olmert said he was ready to begin talks with Palestinian President Mahmoud Abbas.
But his first priority, he said, was the release of the Israeli soldier captured by Palestinian militants earlier this year.
However, he said he attached no conditions to a meeting with Mr Abbas, at that the meeting could actually benefit the captured soldier.
BBC diplomatic correspondent Jonathan Marcus says Mr Blair is intent on a world role despite acknowledging his imminent retirement from office.
He has said he will resign within a year but has not given a firm date for his departure.
'No new plan'
Mr Blair discussed the fragile ceasefire between Israel and Hezbollah and the Israeli-Palestinian conflict.
But Downing Street sources said earlier he was carrying no new plan with him and simply wanted to listen and try to get a measure of the new situation on the ground.
At a news conference with Mr Olmert, he 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.
Testing the water
His refusal to call for an immediate cease-fire during the recent Lebanon crisis, has been seen by his critics as providing perhaps the final nail in his political coffin, our correspondent says.
One of his main aims during this trip was to bolster support for resolution 1701.
He was also seeking to test the waters to see how the broader peace process can be moved forward.
However, the BBC's Matthew Price in Jerusalem says Israel is in no mood for peace negotiations and is also playing down expectations.
The Palestinians, meanwhile, feel that the UK, like much of the international community, has ignored their suffering, and would like Mr Blair to back up his own words about peace here with deeds, he says.