Tony Blair is beginning a two-day visit to Israel on his first mission as special envoy to the Middle East.
Mr Blair will meet a series of key players behind closed doors
Earlier, the former UK prime minister met Jordan's foreign minister in Amman.
Israel has welcomed Mr Blair's visit, but the Palestinian Islamist group Hamas has accused him of bias, and warned him not to ignore them.
Mr Blair's mandate from the Quartet of Middle East negotiators involves trying to strengthen Palestinian institutions, but he cannot negotiate a peace deal.
The Quartet is made up of the European Union, United Nations, US and Russia.
Last week, Mr Blair said he hoped momentum could be regained in the stalled Israeli-Palestinian peace process.
But Mr Blair's mandate is limited, and many Palestinians are sceptical he can make a difference, correspondents say.
Mr Blair's spokesman described talks in Amman as "positive" before he landed in Tel Aviv en route to Jerusalem.
He is expected to meet Israel's foreign and defence ministers on Monday, as well as a top American diplomat.
On Tuesday he is scheduled to meet Israeli Prime Minister Ehud Olmert in Jerusalem and Palestinian Authority President Mahmoud Abbas in Ramallah.
Little public comment is expected from the visit, but officials from all sides made their opinions plain as Mr Blair arrived.
The Palestinian Information Minister, Riad al-Maliki, said Mr Blair had the backing of US President George W Bush and was likely to find Israel more co-operative than previous envoys.
"We are determined to provide whatever is needed from our part in order really to make his mission a successful one," he said.
An Israeli government spokesman said the atmosphere in the region was "positive", but a spokesman for Hamas, which seized control of the Gaza Strip from Mr Abbas' Fatah faction in June, dismissed Mr Blair's chances of success.
"His policy is based on marginalising and bypassing Hamas in support of the leadership of the Palestinian Authority," said Sami Abu Zuhri.
"Any process in the region that marginalises the Hamas movement is doomed to fail."
Mr Blair's mandate does not allow him to talk to Hamas - which the US blacklists as a terrorist group - even though it was elected to government by the Palestinian people last year.
Mr Blair's remit is to encourage reform, economic development and institution-building in the Palestinian territories, to prepare Palestinians for eventually running an independent state.
But the BBC's Middle East editor Jeremy Bowen says that if Mr Blair wants to be more than a fringe player, he will have to get Israel, the Palestinians and the Quartet members talking about final status issues.
Mr Blair says he is optimistic for the future of the Palestinians
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 which the Palestinians also want to make their capital.
At a meeting of the Middle East Quartet in Lisbon last week, Mr Blair said that he planned to "listen, to absorb and to reflect" during his Middle East visit before putting forward any proposals.
"There is a sense that we can regain momentum. That is the crucial thing," he said.