Mr Davutoglu`s AK Party lost its 12-year majority rule in Turkey in elections in June largely because of the success of the pro-Kurdish HDP.
Coalition talks with the nationalist MHP and main opposition CHP failed.
The political uncertainty comes amid rising violence in Turkey and neighbouring Iraq and Syria.
Election `re-run`
President Erdogan will ask Prime Minister Davutoglu early next week to form a temporary power-sharing government, senior officials said.
The Republican People`s Party (CHP), which came second in June`s vote, had asked for a mandate to try to form a new government.
But the president instead opted for what he called a "re-run" of the elections.
Mr Erdogan, who founded the AK Party in 2001, previously denied allegations that he had undermined the coalition talks in order to force a new vote.
June`s result appeared to block his plans to boost the powers of the presidency in Turkey.
An uneasy two-year ceasefire with the PKK fell apart last month, after a suicide bomb blamed on IS killed 32 young activists in the largely Kurdish city of Suruc, close to the Syrian border.
In recent weeks Turkish forces have carried out attacks on militants from the Islamic State (IS) group in Syria and have bombed Kurdish PKK camps mainly in northern Iraq.
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