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 won'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 won't be building all the tens of thousands of housing units that are waiting in the pipeline, but on the other hand we won't be freezing the lives of the inhabitants of the West Bank when we won't freeze the building."
"I don'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 don'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 don't say that, if they don'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.