Jerusalem ( CNN ) -- Israeli Prime Minister Benjamin Netanyahu , who has stopped well short of agreeing to a continued freeze on building Israeli settlements in the West Bank , made comments that suggested that he might be willing to compromise on the issue . Construction of settlements is a major sticking point between Israel and the Palestinian Authority , which recently resumed direct peace talks for the first time since 2008 . `` The Palestinians are demanding that after the 26th of September there will be zero growth in the West Bank , and that wo n't happen , '' Netanyahu said during a Sunday meeting with Middle East Quartet Representative Tony Blair , a diplomatic source briefed on the discussions told CNN . The Quartet consists of the United States , Russia , the United Nations and the European Union . `` Israel will not be able to continue with the moratorium , '' Netanyahu said . `` On one hand , we wo n't be building all the tens of thousands of housing units that are waiting in the pipeline , but on the other hand we wo n't be freezing the lives of the inhabitants of the West Bank when we wo n't freeze the building . '' `` I do n't know if there will be a comprehensive freeze , '' Netanyahu said at a Sunday Cabinet meeting , according to the Israeli newspaper Haaretz . `` But I also do n't know if it is necessary to construct all of the 20,000 housing units waiting to be built . In any case , between zero and one there are a lot of possibilities . '' Last year , Israel instituted a 10-month moratorium on building Israeli settlements in the West Bank . Netanyahu is under pressure from the Palestinians and the from the administration of U.S. President Barack Obama to extend the freeze , which is currently set to expire toward the end of September . Netanyahu 's conservative coalition government wants the prime minister to end the moratorium . An Israeli settlement watch organization called Peace Now says groundwork construction already is complete on 2,000 Israeli housing units in the West Bank , on which building could resume as soon as the moratorium ends . Another 11,000 units have been approved for construction , according to the group . Palestinian Authority President Mahmoud Abbas and Netanyahumet in Washington for direct talks earlier this month . The two pledged in front of the cameras to move the peace process forward , but privately were said to have gotten stuck on the question of whether the Israeli settlements should continue . Abbas and Netanyahu are scheduled for a meeting Tuesday in Egypt , where U.S. Secretary of State Hillary Clinton and George Mitchell , the U.S. special envoy for Middle East peace , are also expected to attend . Netanyahu said that if all sides are serious in their efforts , it would be possible to arrive at a framework for lasting peace within the year . `` Just as we are asked to recognize the Palestinian national state ... we also demand and expect the Palestinians to recognize a Jewish state , the State of Israel , as the national state of the Jewish People . This is the true foundation of peace , '' he said , according to Haaretz . Palestinian negotiators have said they will walk away from peace talks if Israel resumes settlement construction in the West Bank . `` I 'm not demanding as a pre-condition for talks the recognition of Israel as the nation-state of the Jewish people , and I do n't say that , if they do n't do so , I will stand up and leave the negotiating table , '' Netanyahu said , according to the diplomatic source . `` In the same fashion , it 's not logical that the Palestinians are placing pre-conditions and threatening to leave the negotiating table . That is not the way to move forward seriously to a peace agreement . '' CNN 's Kevin Flower contributed to this report .
Israel is under pressure to extend the UN moratorium on settlements in the West Bank . The settlements issue has emerged as a major sticking point in peace negotiations . Housing watch group : Israel has already laid groundwork for 2,000 housing units .