In his message on Tuesday, Erdogan reiterated Ankara's "determination to work closely with the US administration" in the coming period, Anadolu Agency reported.
He said "the strong cooperation and alliance" between the two countries would continue to contribute to world peace.
The Turkish presidency said on Tuesday that Erdogan had sent a message to Trump as well.
"No matter how the official election results manifest, I thank you for the sincere and determined vision you have put forth for Turkey-US relations to develop on the basis of our mutual interests and values during your presidency in the last four years," Erdogan said in the message.
Analysts have said the US-Turkish relations could be further strained under a Biden administration, concerns that have also led to a decline in Turkey's lira.
