The Yesha Council, a Jewish settler group, has warned that Israel's ruling coalition could collapse if the government continues a freeze on settlement building.
Palestinians say they will walk out of the talks if construction resumes.
Peace talks are to resume on Tuesday. A partial freeze on Israeli settlement building in the occupied West Bank is due to expire on 26 September.
The Palestinians say they will walk out of the talks if construction resumes.
On Friday, US President Barack Obama said he had urged Prime Minister Benjamin Netanyahu to continue a partial construction freeze in the settlements as the best way of helping talks to progress.
But Yesha Council chairman Danny Dayan warned that the talks are doomed to failure over the issue of settlements.
"If this government does not abide by its promises, then it will not be able to continue to govern," he said.
The council represents many of the 400,000 Israelis who live in illegal Jewish settlements on the Palestinian West Bank and in Arab East Jerusalem.
In a statement, the council said that "any continuation of the construction freeze would lead to severe political instability within Israel and the ultimate collapse of the current government".
Palestinian government spokesman Ghassan Khatib has again called on the Israeli government to end all settlement activity, saying it was endangering the peace process.
"Israel should stop all kinds of settlement activities in order to give a chance for negotiations," Mr Khatib told the BBC.
"Any Israeli settlement activities is a threat to the newly-established Israeli-Palestinian peace process."
An initial round of talks was held in Washington on 2 September. It was the first direct Israeli-Palestinian talks in nearly two years.