The Turkish president's office said both leaders agreed that Khashoggi's killing needed to be clarified "in all aspects".
Earlier, Saudi Arabia's foreign minister Adel al-Jubeir had said that Khashoggi's death occurred as a result of a "rogue operation" where individuals ended up "exceeding their authorities and responsibilities".
Saudi Arabia had earlier denied any involvement in the disappearance of Khashoggi who was last seen entering the Saudi consulate in Istanbul on October 2nd.
Jubeir said Saudi Arabia did not know where Khashoggi's body was while admitting that his killing was a "tremendous mistake".
Meanwhile, President Trump said that US-Saudi relationship will "whether this" while asserting that "when the investigation is over and the facts are revealed, people know who is responsible."
The US president added that King Salman is determined to see this "investigation through and determined to ascertain the facts and hold those responsible accountable."
King Salman, father of Crown Prince Salman has begun to take a personal interest in the case after the disappearance of Khashoggi hit international headlines as Turkish officials privately blamed the Saudi government for Khashoggi's disappearance.
In another related development, Istanbul governor's office has put Hatice Cengiz, the fiancee of Khashoggi under 24-hour police protection. Cengiz was outside the Saudi consulate when Khashoggi entered the Saudi consulate and never came back.
After Saudi Arabia confirmed his death, she wrote on Twitter in Arabic: "They have taken your body from this world, but your beautiful smile will stay in my world forever."
Khashoggi wanted to submit divorce papers to the consulate and marry Cengiz, a Turkish citizen, even as her fiancee waited outside for hours but the Washington Post columnist who was a long-time critic of the Saudi government, never came out of the consulate and was widely believed to have been killed inside the consulate premises.