Turkish officials have said they believe Khashoggi, 59, a critic of the Saudi leadership and a contributor to The Washington Post's Global Opinions section, was killed by a team of 15 Saudis flown in specifically to carry out the attack.
"Based on their initial findings, the police believe that the journalist was killed by a team especially sent to Istanbul and who left the same day", the government source said on Saturday.
Erdogan's comments were his most direct suggestion yet of potential Saudi culpability in Khashoggi's disappearance and came after other Turkish officials have said they believe that he was killed by Saudi agents inside the consulate.
A senior Turkish police source told Middle East Eye that police believed that Khashoggi was "brutally tortured, killed and cut into pieces" inside the consulate after visiting the building on October 2.
'The official strongly denounced these baseless allegations, ' the agency wrote. Turkish officials say they believe Khashoggi is being held inside the consulate building, which they can not search without an invitation.
"His disappearance could exacerbate tense relations between Turkey and Saudi Arabia, which worsened a year ago after Turkish President Recep Tayyip Erdogan called the Gulf States" isolation of Qatar "inhumane and against Islamic values.' In the spring, Saudi Crown Prince Mohammed bin Salman described Turkey as one part of a 'triangle of evil' with Iran and Islamic extremists".
Earlier on Saturday Turkish officials said prosecutors had begun investigating Khashoggi's disappearance and a spokesman for President Tayyip Erdogan's AK Party said authorities would uncover his whereabouts.
Saudi officials repeatedly said the deal was "on track, on time" for the second half of 2018, but earlier this year they said it would be delayed into 2019.
'Jamal was - or, as we hope, is - a committed, courageous journalist.
In a statement on Sunday, Mutasem Khashoggi, the legal adviser to the Khashoggi family in Saudi Arabia, told Al-Arabiya news that he believed external parties were using his brother's disappearance to "push their agenda".
Speaking to CNN Turk, Aktay said that Khashoggi's friends had told him to not go to the Saudi embassy and that the consulate was "not safe".
Although Khashoggi was planning to move to Istanbul, he was also a legal resident of the United States and a contributing columnist for The Washington Post.
State Department senior officials have spoken with Saudi Arabia through diplomatic channels about the matter, the top USA diplomat added.
A Saudi delegation had arrived in Istanbul to assist with the investigation, the statement said.
Reporters Without Borders (RSF) said on Twitter that if reports of his death were confirmed, "this would constitute a horrific, utterly deplorable, and absolutely unacceptable assault on press freedom".
Khashoggi's criticism of Prince Mohammed's policies have appeared in both the Arab and Western press.
The crown prince, in an interview with Bloomberg on Friday, offered to allow Turkish authorities to search the Saudi consulate in Istanbul, saying: "We have nothing to hide".
The official quoted by SPA underlined that Saudi Arabia was responsible for the safety and well-being of all its citizens, wherever they may be, and that its authorities "are diligently following up on this matter to uncover the complete facts".
Saudi Arabia has since March 2015 spearheaded a regional military intervention in Yemen, in support of a government that is fighting rebels backed by Riyadh's arch-rival Iran.