The Israeli government had contacted Ankara in early December and asked Turkey to help in persuading Hamas to agree to an extension of the ceasefire, the sources said.
The operation to crackdown on Hamas, which started on Saturday, has so far killed 315 people, including 51 civilians according to the United Nations, with hundreds more reportedly injured. Israel considers various options including an all-out invasion.
Abbas had also made a similar demand from Turkey and sent the Fatah parliamentary group leader, Azzam al Ahmad, to Ankara to deliver his request. Al Ahmad had met with Ahmed Davutoglu, the Turkish prime minister's top foreign policy advisor.
Al Ahmad also asked Turkey to mediate between Hamas and Fatah, the sources added. He also said the Palestinians had expected Turkey to play a similar role in mediation between Israel and Palestine, as it did between Israel and Syria.
Turkey, however, rejected the demands, saying it would be difficult to achieve concrete results in the current situation, the foreign ministry officials said.
Israel's operations against Gaza incited fears of a wider conflict in the region. Israel says the operations are in response to Hamas attacks which began again after the end of a six-month long ceasefire.