"My wish is to have friendly and not hostile relations" with the United States, Erdogan said on the sidelines of the UN general assembly in New York, according to AFP.
"But the way things are going between two NATO allies is currently not too auspicious," he added.
Erdogan said had "worked well" with previous US presidents, George W. Bush, Barack Obama and Donald Trump "but I cannot say things have gotten off to a good start with Biden".
Relations between the US and Turkey soured before Biden took office, after Turkey's purchase of the Russian S-400 missile defense system that the US believes can be used to spy on Western defenses.
In response to the purchase, the US sanctioned Turkey’s military procurement agency and expelled Turkey from the F-35 program, under which Western allies produce the next-generation fighter jet's parts and secure its early purchasing rights.
Turkey has repeatedly made clear it will use the Russian system despite US threats of sanctions.
"We bought the F-35, paid $1.4 billion and the F-35 were not delivered to us," Erdogan said on Thursday.
"For us the S-400 affair is done. It is not possible to go back on that. The United States must understand. We, Turkey, are honest, but unfortunately the United States were not and are not," he added.
The relations with the US became more complicated when Biden, who has also made a point of highlighting Turkey's deteriorating record on human rights, took three full months after his swearing-in ceremony before placing his first call to Erdogan.
That phone call was to inform him that Washington was recognizing the Armenian genocide by the Ottoman Empire during World War I.
Erdogan denounced the move and urged Biden to swiftly reverse it, advising the United States to "look in the mirror".
In June, Erdogan and Biden held what the Turkish President described as a "fruitful and sincere" meeting on the sidelines of the NATO summit in Brussels.
