The phone call came on the eve of the G20 leaders' summit hosted by Riyadh on Saturday and Sunday.
Erdogan and the Saudi king discussed bilateral relations during the phone call and exchanged views on the G20 summit, the Turkish presidency said late on Friday< AFP reported.
The Turkish leader is due to address the summit via video link at 1300 GMT.
"President Erdogan and King Salman agreed on keeping channels of dialogue open in order for the bilateral relations to be enhanced and for issues to be settled," it added.
Turkey and Saudi Arabia have long competed for supremacy in the Muslim world but the tensions between the two regional powers have intensified since the 2018 murder of Washington Post contributor Khashoggi at the kingdom's Istanbul consulate.
The case has sparked an international outcry and tarnished the global reputation of Crown Prince Mohammed bin Salman known as MBS.
Khashoggi was strangled and his body cut into pieces by a 15-man Saudi squad inside the consulate, according to Turkish officials. His remains have not been found.
Erdogan has said the order to murder Khashoggi came from "the highest levels" of the Saudi government but has never directly blamed Prince Mohammed.
In September, a Saudi court overturned five death sentences issued after a closed-door trial in Saudi Arabia that ended last year, sentencing them to 20 years in prison instead.