Palestinian officials have rejected an offer by the Israeli government to halt settlement construction if they recognise Israel as a "Jewish state".
The Palestinians said they already recognised the state of Israel, and that the real issue threatening peace talks was illegal settlement activity.
Israel has been under international pressure to renew its partial freeze on construction in the occupied West Bank.
The Palestinians have threatened to walk out of the talks over the issue.
The direct negotiations only resumed last month after a 20-month hiatus, and no meeting has been held since the freeze ended on 26 September.
In a speech to the Israeli parliament on Monday, Prime Minister Benjamin Netanyahu said: "If the Palestinian leadership will say unequivocally to its people that it recognises Israel as the nation-state of the Jewish people, I will be prepared to convene my cabinet and request an additional suspension of building for a limited period of time."
"Undoubtedly such a step by the Palestinian Authority would be a confidence-building measure that will open a new horizon of hope as well as trust among broad parts of the Israeli public," he added.
Mr Netanyahu said he had made the offer to the Palestinian Authority "in quiet ways" last month, but that it had been rejected.
The chief Palestinian negotiator, Saeb Erekat, said Mr Netanyahu was "playing games" with his offer, and that there was no connection between settlements and the national character of Israel.
"I don't see a relevance between his obligations under international law and him trying to define the nature of Israel," he added. "I hope he will stop playing these games and will start the peace process by stopping settlements."
Israel has occupied the West Bank, including East Jerusalem, since 1967, settling close to 500,000 Jews in more than 100 settlements. They are considered illegal under international law, although Israel disputes this.
Palestinian officials say recognising Israel as a Jewish state would compromise the rights of 20% of the Israeli population that is not Jewish, and undermine the claims of Palestinian refugees to return to their former homes in Israel.
They also note that the Palestine Liberation Organisation (PLO) formally recognised "the right of the State of Israel to exist in peace and security" in an exchange of letters before the signing of the 1993 Oslo accords.
In Israel's peace treaties with Egypt and Jordan there was no mention of recognition of Israel as a Jewish state.
The US state department did not respond directly to Mr Netanyahu's offer, but said the US position on settlements had not changed.
"As we've noted we would like to see the settlement moratorium extended. Beyond that, we are not going to get into the substance of our discussions with the parties," a spokesman told the Haaretz newspaper.
The BBC's Wyre Davies in Jerusalem says Mr Netanyahu's offer was an attempt to wrest back the initiative in arguments over the settlement freeze.
Earlier, Mr Netanyahu's government backed a bill requiring that a referendum be held before any territory could be yielded in a peace deal.
On Sunday, the prime minister angered Israeli Arab leaders when his cabinet approved the submission of a bill to parliament that would require new citizens to pledge allegiance to Israel as a "Jewish and democratic state".
It came two days after the Arab League backed a Palestinian pledge not to return to direct talks without a full settlement construction freeze, but also gave the US a month to come up with a way to save the negotiations.