Erdogan also said Saudi Arabia's public prosecutor was due in Istanbul on Sunday to meets its regional chief prosecutor.
Saudi Arabia's public prosecutor has said the killing of journalist Jamal Khashoggi in the kingdom's consulate in Istanbul was premeditated, reversing previous official statements that his death was unintended.
Saudi Arabia's foreign minister has described the kingdom as a "vision of light" in the region as it tries to control the fallout from Jamal Khashoggi's killing - its biggest diplomatic crisis since the 9/11 attacks.
The Saudi state is responsible for the murder of journalist Jamal Khashoggi and can not "wash its hands" of responsibility, UN Special Rapporteur on Extrajudicial, Summary or Arbitrary Execution Agnes Callamard said at the UN headquarters in New York City on Thursday.
Salah Khashoggi's departure from Saudi Arabia came a day after a meeting at the al Yamama Palace in Riyadh in which he and other family members received condolences from King Salman and the crown prince.
"And what we say to people is wait until everything is done, then reflect on the results of the investigation, and then make a determination on whether this investigation was serious or not".
Central Intelligence Agency director Gina Haspel was in Turkey earlier this week to review evidence, and she briefed U.S. President Donald Trump in Washington on Thursday.
Afghans turn out for delayed vote
According to police, a suicide bomber on foot detonated his explosives close to the gate of the offices. According to the election commission, 567,000 people have registered to vote in Kandahar .
The foreign minister of Saudi Arabia has characterized the global outrage in response to the killing of journalist Jamal Khashoggi as "fairly hysterical".
"If I knew something like this would happen, I would have agreed to not marry him and would never have wanted him to go inside", she said in Turkish during the interview, crying several times.
Turkish media have published a series of grisly revelations about the murder.
Khashoggi was least seen entering the Saudi consulate in Istanbul on 2 October to complete paperwork for his wedding to his Turkish fiancee, Hatice Cengiz.
Turkish officials suspect Saudi agents killed Khashoggi, 59, inside the consulate and cut up his body. All four of Khashoggi's children are now in the U.S. On Tuesday, Pompeo announced that 21 Saudi "suspects" would have their US visas revoked or be deemed ineligible for a USA visa for their role in the murder.
Trudeau said he might cut off any arms export permits that allow Canadian manufacturers of military equipment to ship their goods to Saudi Arabia.
During the vigil, a friend of Khashoggi and advisor to Turkish President Recep Tayyip Erdogan, Yasin Aktay, said that "no one can sweep this affair under the rug".