But Palestinians note that Israel's previous peace deals with Egypt and Jordan didn't require acceptance of Israel's Jewish character.
Further, they complain, there are no clear definitions of a "Jewish state." Would Arab Israelis have an inferior status or reduced rights in a Jewish state? Would such an endorsement affect the right of return for Palestinian refugees or the division of Jerusalem?
"Would this mean they could get rid of all non-Jews from Israel?" Palestinian negotiator Nabil Shaath asked. "They have never explained the meaning. They are using this to just create new complications. Now, rather than discussing borders or Jerusalem, we are talking about the Jewishness of the state."
Even Israelis don't agree on what "Jewish state" should mean, Palestinians say. Secular Israelis worry such terminology would increase the mix of religion and state. Many Orthodox Jews, meanwhile, believe the Torah forbids the formation of a Jewish state until the arrival of the Messiah. The lack of consensus is one of the reasons Israel never drafted a constitution.
Some Palestinian leaders have expressed a willingness to consider calling Israel a Jewish state, provided the term is defined and other issues are resolved. Shaath said that if Israel is serious it should raise the issue formally during negotiations, rather than in political speeches and in the media.
"They should bring it to the table," he said. "But right now, they are using it to create fear and agitation."
Batsheva Sobelman in The Times' Jerusalem Bureau contributed to this report.