The resignation of the US-educated economist, who won international acclaim for his state-building efforts, came despite US efforts to head off the crisis, with Secretary of State John Kerry making a personal intervention late on Friday.
It also came just days after Kerry made a fresh push to revive long-dormant peace talks with moves to revive the West Bank economy.
Speaking in Tokyo, Kerry expressed regret over Fayyad’s resignation on Saturday night and urged Abbas to find the right person to take on the tough job and work with Washington.
“Would I prefer that he weren’t leaving? Sure, because you have continuity,” he said, noting Fayyad had “made a huge difference” and expressing hope Abbas would find “the right person to work with him … and to work with us, and establish confidence.”
Abbas accepted Fayyad’s resignation at a brief meeting at the Muqataa presidential compound in Ramallah, but officials said he had asked the 61-year-old to stay on in a caretaker role until a new premier can be appointed.
So far, there is no clear frontrunner to take up the post which has been held by Fayyad since 2007.
Possible successors include Mohammed Mustafa, head of the Palestine Investment Fund, and businessman and former economy minister Mazen Sinokrot who has good relations with Gaza’s Hamas rulers.
Abbas himself could also take on the role within the framework of a “national unity government” as foreseen by a reconciliation agreement between the Islamist movement Hamas and the president’s Fatah movement.
Rumors that Fayyad would either resign or be told to step down by Abbas have been rife in recent weeks after long-standing differences between the two came to a head over the finance portfolio.
Fayyad, a political independent, had come under increasing criticism as the Palestinian Authority lives through its worst-ever financial crisis, with Fatah openly deriding his economic policies as “confused”.
Long-running tensions between Fayyad and Abbas came to a head six weeks ago over the resignation of finance minister Nabil Qassis, with Fayyad accepting it while Abbas did not.
Fayyad himself was finance minister for five years from 2002, and after being appointed premier in 2007 he continued to hold both portfolios until Qassis took over in May 2012.
He was deeply unpopular with Fatah, with a top official from the party’s Revolutionary Council on Sunday expressing relief at his departure.
“Fatah is relieved over Fayyad’s timely resignation which was inevitable,” said secretary general Amin Maqbul, saying his government had “failed miserably” to steer the economy through the economic crisis.
Commentators said the problem stemmed from the fact that Fayyad did not belong to Fatah.
Abbas’ PA is in the grip of its worst-ever financial crisis due to a shortfall in promised foreign aid and Israel’s withholding of tax monies for several months, although that decision was recently reversed.
On the street, opinion over his resignation was divided.
“I’m against Fayyad’s resignation because I consider him to be one of the best economists, and the Palestinian government has lost him,” said 23-year-old Raed al-Khatib from Ramallah.
“The economic crisis is not just about the Palestinian people, everyone is suffering, even the Europeans.”
Others said it was a chance to bring in a new face.
“I’m optimistic,” said 53-year-old Mohammed Amin from Jerusalem. “People here are tired and are suffocating (from the crisis) and, God willing, the next person will bring people some economic relief.”
Although there was no comment from Israel, Haaretz newspaper said senior political figures “expressed much regret” over Fayyad’s departure.
“Without Fayyad guarding the public coffers, it’s not certain that the countries currently providing the Palestinian Authority with aid will continue to do so,” it said.