Similar demands have been made of the Palestinian Authority in the past, but the body says it will only recognize Israel as it existed before 1967, prior to the Jewish state seizing control of the West Bank and Gaza Strip in the Six Day War.
Meanwhile, stark differences between US and Israeli policies emerged during the first meeting between President Barack Obama's Middle East envoy and the new Israeli leadership which took office in late March.
Special envoy George Mitchell made it clear Washington is aiming for the creation of a Palestinian state.
"US policy favors, with respect to the Israeli-Palestinian conflict, a two-state solution," Mitchell told reporters in Jerusalem on Thursday.
New tack needed
New Israeli Foreign Minister Avigdor Lieberman observed that past Israeli concessions have led to violence, not peace.
Lieberman told reporters that the peace process with the Palestinians "had reached a dead end" and that new ideas must be found.
"The traditional approach has so far led to no solutions or results," Lieberman said.
Mitchell is expected to travel to the West Bank for talks with Palestinian Authority President Mahmoud Abbas of the Fatah party and other officials on Friday.
More rocket fire
Israeli aircraft bombed a house in the Gaza Strip on Thursday - the first strike in more than a month on the densely populated area. No casualties were reported.
The raid came one day after Gaza militants fired a rocket into southern Israel.
Both Israel and the Palestinian militant group Hamas have failed to observe the ceasefires they announced in mid January to end a deadly 22-day war.
According to a Palestinian rights group, nearly 1, 500 Palestinians, including 926 civilians, were killed in the fighting. Israel, however, disputes those figures.