The former UK prime minister's spokesman said Mr Blair was on "listening mode" for the two-day trip.
His mandate from the Quartet of Middle East mediators is to work to strengthen Palestinian institutions, without trying to negotiate a peace deal.
The Quartet is made up of Russia, the UN, the EU and the United States.
After a stop in Jordan on Monday, Mr Blair, who stepped down as prime minister in June, met Israeli Foreign Minister Tzipi Livni in Jerusalem.
On Tuesday, Mr Blair goes to Ramallah in the West Bank to meet the Palestinian Authority President Mahmoud Abbas and Prime Minister Salam Fayyad. He then returns to Israel for talks with Israeli Prime Minister Ehud Olmert.
Last week, Mr Blair said he hoped momentum could be regained in the stalled Israeli-Palestinian peace process.
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