In his first major public challenge to Erdogan since leaving office three years ago, Davutoglu, in a 15-page statement issued on Monday, blamed policy changes and an alliance with the Nationalist Movement Party (MHP) for losing votes in major cities.
"The election results show that alliance politics have caused harm to our party, both in terms of voter levels and the party's identity," the statement read.
The AKP and the MHP formed an alliance before presidential and parliamentary elections in June 2018 in which Erdogan won the executive presidency. Support for his party, however, declined.
The 31 March elections saw Turks voting to elect mayors, municipal councils, and other local officials. Erdogan’s AKP secured an overall victory with some 51 percent of the votes.
The ruling party, however, suffered major defeats in the elections, which handed a victory to the main opposition Republican People's Party (CHP) in the political power base, Ankara, and the third-largest city of Izmir.
The city of Istanbul seems to have come out from under the AKP's 25-year rule as the results showed the CHP had narrowly won control of the country's economic, cultural and historic center.
Erdogan began his political career as mayor of Istanbul, Presstv reported.
In 2017, the Turkish people voted in a referendum on a new presidential system promoted by the sitting leader. The latest local elections serve as a test for that leadership scheme, which awards sweeping powers to Erdogan.
Elsewhere in his statement, the former prime minister criticized the AKP's economic policies, media restrictions and the damage he said it had done to the separation of powers and to institutions.
Davutoglu, a high profile figure, served as Turkey's prime minister between 2014 and 2016, when a falling-out with Erdogan occurred.
In recent years, Turkey's political sphere has been freighted with media speculation that prominent AKP politicians such as Davutoglu might break away to establish a new party.
"I call on our party's executives and relevant bodies to assess all these subjects and our future vision sensibly and with cool heads," Davutoglu stated.