Electoral board head Sadi Guven said votes were still being counted and objections taken into account.
But Istanbul was a tight race and both Yildirim and the opposition CHP candidate Ekrem Imamoglu claimed victory in the early hours of Monday.
Ballot counts were still under way Monday morning in an anxious wait for Istanbul, Turkey's largest city and commercial hub.
The AKP and its Islamist predecessor have controlled Istanbul and the capital Ankara for 25 years.
Turkish President Recep Tayyip Erdogan's party has challenged the results of the local elections in the country's two biggest cities, where preliminary results show narrow victories for the opposition candidates.
Dr. A. Kadir Yildirim, a fellow for the Middle East at the Baker Institute for Public Policy at Rice University, in his comments to Sputnik expressed opinion that such results of the municipal elections were absolutely not expected by the ruling AK Party.
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Unofficial results reported by Anadolu showed Mansur Yavas, the candidate of the CHP, winning the top post in Ankara.
Even though Erdogan is firmly entrenched in an all-powerful presidency after winning re-election previous year, political analysts do see the elections for mayors and city councils as a referendum on what is described as his authoritarian style of rule.
President Erdogan is to contest more than 300,000 votes in Istanbul, which his party lost to the main opposition in local elections. The opposition also increased its support along the Mediterranean, taking the city of Adana from the nationalists and the resort destination of Antalya from the ruling party.
It also retained its hold over Izmir, Turkey's third largest city, located on the Aegean Sea.
A strategic decision by a pro-Kurdish party to sit out critical races in major cities contributed to the opposition's gains.
Dr. Demiralp concluded that the government realizes that losing Istanbul and Ankara is a major setback and if the CHP party mayors perform well in the next four years this could cost the AK Party the general elections.
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Erdogan's ruling alliance, including the nationalist MHP, captured 51.7 percent of the nationwide vote with almost all votes counted, according to state-owned Anadolu news agency.
"This will certainly lead to an emerging new political landscape in Turkey", he said.
Both Erdogan and Finance Minister Berat Albayrak, the president's son-in-law, have promised to implement reforms after the elections to address economic woes.
In a Monday statement, Iranian Foreign Ministry Spokesman Bahram Ghasemi congratulated neighboring Turkey over the successful holding of local and municipality elections, noting that democracy in the regional countries is the guarantee for the region's independence, security and stability.
Ali Ihsan Yavuz, an AKP deputy chairman, called the elections "one of the most stained in our democratic history" - a claim the opposition Republican People's Party, or CHP, quickly rejected.
The government has replaced 95 elected officials since 2016 for alleged links to outlawed Kurdish militants.
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"There is still three days for objections", he added, implying that a final result will take some time.