It has been put back until after a visit by Abbas to Kuwait on Monday, an official told AFP on condition of anonymity.
Abbas and Fayyad have been at loggerheads as criticism of the prime minister’s economic policies has mounted in the ruling Fatah movement but Washington has lobbied hard for the US-educated economist to remain in post.
Late on Friday, US Secretary of State John Kerry telephoned Abbas to press him to find common ground with his prime minister, Palestinian officials said.
Rumors that Fayyad would either resign or be told to step down by Abbas have been rife in recent weeks after longstanding differences between the two men came to a head over the finance portfolio.
Finance minister Nabil Qassis announced on March 2 that he was standing down. Fayyad agreed to the resignation but Abbas, who was abroad at the time, rejected it.
Fayyad held the finance portfolio as well as the premiership before Qassis’s appointment in May 2012.
A planned meeting Thursday at which a senior Fatah official had said Fayyad intended to hand in his resignation was also postponed after Washington insisted that to the best of its knowledge the prime minister was “sticking around”.
Last week, the Fatah Revolutionary Council for the first time openly criticized the Fayyad government’s economic policy.
Abbas’ Palestinian Authority is in serious financial crisis, partly as a result of non-disbursement of promised foreign funding, although the US Congress quietly unblocked $500 million in aid last month.
The international community credits Fayyad with building a sound institutional framework for the Palestinian Authority in the areas of the occupied West Bank under its control.
His resignation could hamper implementation of an agreement with Israel which Kerry announced this week to “promote economic development in the West Bank.”