It was the second time within 10 weeks that a Palestinian prime minister has tendered his resignation over an internal power struggle, and Abbas now has 35 days to find a replacement, officials said.
Abbas's acceptance of Hamdallah's resignation was first disclosed to AFP by a senior Palestinian source but was quickly confirmed by Abbas's spokesman Nabil Abu Rudeina in a statement published by the official WAFA news agency.
"The president of the state of Palestine Mahmud Abbas today accepted the resignation of prime minister Rami Hamdallah and asked him to continue on in a caretaker role until the formation of a new government," the statement said.
"President Abbas has accepted the resignation of Hamdallah after he refused to work with two deputies," the source told AFP, speaking on condition of anonymity.
"He asked him to stay on in a caretaker role until he chooses someone else to form a new government."
The crisis erupted on Thursday when Hamdallah unexpectedly tendered his resignation over what government officials said was a "power struggle" resulting from Abbas's decision to install two deputies working directly under him.
Hamdallah had withdrawn his resignation on Friday during what a high ranking government official said was a "positive" two-hour meeting with Abbas.
But today morning, the situation was beyond repair with Abbas taking the decision to accept Hamdallah's resignation.
"Hamdallah initially agreed to withdraw his resignation (on Friday) but he insisted yesterday during a meeting with the president on either not having any deputies, or having deputies with restricted powers," the source said.
"This led to a sharpening of the dispute over the powers of the prime minister, which ended up with the president accepting his resignation."
At the heart of the crisis is a dispute over the division of responsibilities within government.