If these results are confirmed, they will demonstrate a decline for President Erdogan, who has dominated in the polls since his becoming Prime Minister in 2003.
"[During the phone call], they have touched upon the issues on the bilateral agenda in the context of the preparations for the planned eighth session of the High-Level Russian-Turkish Cooperation Council to be held in Moscow on April 8", the press service stated.
Erdogan, for his part, expressed thanks to Aliyev for his honest wishes during the conversation in which both leaders affirmed that the friendship and fraternal ties between Baku and Ankara would continue to increase.
Erdogan portrayed the election as a victory for AKP, which along with coalition partner, the rightwing Nationalist Movement Party (MHP), won around 52 percent of the votes nationwide.
In Istanbul, the county's largest city, the CHP mayoral candidate was more than 25,000 votes ahead of his AKP opponent as the last votes were being counted, according to the country's electoral board and CHP data.
In Istanbul, the main opposition candidate, Ekrem İmamoğlu, said in the early hours of Monday that he had won by almost 28,000 votes over the AKP candidate and former prime minister, Binali Yıldırım.
Earlier on Sunday, Erdogan appeared to admit that his party might lose Istanbul, while nevertheless hailing the conservatives' overall performance at the local elections.
The AKP and its Islamist predecessor have controlled Istanbul and Ankara for 25 years.
Thousands attend remembrance service for Christchurch mosque attacks
Ardern will address the service, which has the theme "We Are One" and will be broadcast on national television. Thousands more were expected to attend a service at Auckland's Eden Park on Friday afternoon.
Mansur Yavas obtained 50.9 percent of the vote, while AKP's Mehmet Ozhaseki had won 47.06 percent, with 99.8 percent of the ballots counted, the Hurriyet Daily news reported.
Speaking at a news conference in Istanbul, Erdogan said the next elections would be held in June 2023 and that Turkey would carefully implement a "strong economic programme" without compromising on free market rules.
The results, which were still being tallied and faced appeals, would likely bring personnel changes at the highest ranks of government, according to sources inside and close to the AKP.
The poll was the first municipal election since Turks gave Erdogan wide powers in 2017 by approving constitutional reforms to create an executive presidency, and many saw the vote as a test of the strength of Erdogan and the AKP. Election campaigns are a chance for Mr Erdogan to travel across his vast country, showcasing the populist genius that has kept him at the top of Turkish politics for 16 years.
If the opposition won in Istanbul, Turkey's largest city and commercial hub, that would be a watershed moment. That means that out of some 10 million ballots cast in the city, the difference at the time was about 5,000 votes.
Turkey's economy has been declining following a currency crisis a year ago when the lira lost more than 30% of its value.
But in a sign of possible turmoil ahead, AKP officials said they would challenge the alleged invalidation of tens of thousands of votes in both cities.
Erdogan has waned at rallies that if the opposition candidate wins in Ankara, residents would "pay a price" and accused his rivals of terrorist supporters aiming to ruin Turkey.