"Abbas on Tuesday met head of the caretaker government Rami Hamdallah and tasked him again with forming a government," the Palestinians' Wafa news agency quoted Abbas spokesperson Nabil Abu Rudeina as saying.
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Hamdallah's office said in a statement he had accepted the task and would form a new government within five weeks.
Abbas accepted Hamdallah's resignation on June 23 after barely two weeks on the job, but asked him to stay on as a caretaker until a new premier could be appointed.
The Palestinian leader initially had five weeks to find a replacement, officials said, but the date -- which would have ended in late July -- was put back to August 14 due to the Muslim holy month of Ramadan which started on July 10.
Hamdallah, who was sworn in on June 6, had been incensed by Abbas's decision to create two new deputy prime minister posts under him, sources in his office said on June 23.
It was the second time in 10 weeks that a prime minister had tendered his resignation over a power struggle.
In April, then Premier Salam Fayyad tendered his resignation following a power struggle with Abbas over the finance portfolio.
Hamdallah's June appointment was seen as an interim measure until Abbas could piece together the long-awaited national unity government foreseen by a 2011 reconciliation agreement between his Fatah movement and its Islamist rival Hamas , which rules Gaza.
Tuesday's announcement came on the eve of new peace talks between the Palestinians and Israel in Jerusalem following the resumption of direct negotiations in Washington last month ending a three-year break.
Hamas, which refuses to recognize the West Bank-based Palestinian Authority prime minister, is strongly opposed to the resumed peace talks, complicating reconciliation efforts.
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