Fayyad was expected to meet Abbas in the city of Ramallah, after PA chief’s return from a regional tour to Qatar and Jordan, to submit his letter of resignation.
The relationship between Fayyad and Abbas has been tense for some time over differences on the policies of the Palestinian Authority with Abbas.
Palestinian sources say already strained relations between Fayyad and Abbas became worse last month after the prime minister accepted the resignation of Finance Minister Nabil Qassis, despite opposition from Abbas.
Last year, the prime minister told Abbas that he was eager to quit.
There have been also rumors about Abbas’s decision for replacing Fayyad with Mohammad Mustafa, the chairman of Palestine Investment Fund.
Fayyad has served as the prime minister of the Palestinian Authority since 2007.
The self-rule government administers 38 percent of the occupied West Bank.
Abbas appointed Fayyad to his post after the Hamas Movement took control of the Gaza Strip in 2007.