Kilicdaroglu, chair of the secularist Republican People's Party (CHP), received 44.9% in what was seen as the biggest electoral challenge to Erdogan's 20-year rule.
A third candidate, nationalist Sinan Ogan, obtained 5.17% and both Erdogan and Kilicdaroglu are expected to seek his endorsement in negotiations this week.
Turkey hosts the world's largest refugee population of around 4 million, according to official figures.
Supporters of Kemal Kilicdaroglu, presidential candidate of Turkey's main opposition alliance, rally outside the Republican People's Party (CHP) headquarters on election night in Ankara, Turkey May 14, 2023.
In Wednesday's video, Kilicdaroglu also accused Erdogan of cooperating with the network Ankara accuses of orchestrating a 2016 coup attempt.