"Hamdallah met Abbas for two hours in the president's headquarters in Ramallah and informed him he had decided to withdraw his resignation," the official told AFP on condition of anonymity.
Palestinian officials and media had reported a "power struggle" as being the reason for Hamdallah's offer to quit, with the premier incensed by Abbas's decision to appoint two deputy prime ministers in a government that was formed on June 6.
"Hamdallah wants clear and defined powers as prime minister and for his deputies, based on the law, so his authority is not encroached on," the official said, adding that the meeting had been "positive."
Hamdallah presented his resignation yesterday, only two weeks after taking office, in the latest crisis for the Palestinian Authority.
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His appointment on June 2 had followed the resignation of his predecessor Salam Fayyad, a Western-backed economist who quit after a spat with the Palestinian president.
Fayyad resigned in April but stayed on as caretaker prime minister upon request from Abbas.
Hamdallah, an independent considered close to Abbas's ruling Fatah faction who was also secretary general of the Central Election Commission, pledged after his nomination to follow a similar path to Fayyad and said he would leave the government line-up largely unchanged.