"I think there is a sense of possibility, but whether that sense of possibility can be translated into something, that is something that needs to be worked at and thought about over time," Blair, former U.K. prime minister, told a news conference in Israel, on arrival Monday.
The envoy of the Quartet, comprising the UN, the EU, the U.S. and Russia, said he had come there "to listen, to learn and to reflect" about the situation during his visits to Jordan, Israel, and the Palestinian territories.
The Quartet approved Blair as special envoy June 27. His mandate does not allow him to conduct talks with representatives of Islamist group Hamas.
Palestinian territories underwent a de facto split after Hamas gained control over Gaza in armed confrontations with the pro-presidential Fatah movement.
Blair's duties in the new position will include the mobilization of international aid to Palestinians, the elaboration of a plan on economic development for the Palestinian National Authority (PNA), and ensuring cooperation with other countries to achieve the Quartet's aims.
A leading Russian expert said earlier that naming Blair as the Middle East Quartet's special envoy was a poor choice.
"The appointment of Tony Blair as the Middle East Quartet's special envoy was the worst possible choice for the region," the vice president of the Geopolitical Problems Academy, Vladimir Anokhin, told a RIA Novosti news conference Friday.