Erdogan told reporters that authorities were looking into all camera records and monitoring incoming and outgoing airport transits, but added that Turkey would await the results of the prosecutor's investigation.
The Committee to Protect Journalists Deputy Executive Director Robert Mahoney said in a statement that that the group was "alarmed" by the reports that Khashoggi may have been killed inside the consulate.
"God willing we will not be faced with the situation we do not desire", he added.
The source said the team was at the consulate that same day and later left Turkey for Saudi Arabia.
He had sought assurances from friends, given a number for his fiancee to call if he failed to reappear - and even received an overture to return to Riyadh from Mohammed bin Salman himself.
Jamal Khashoggi, the prominent Saudi journalist missing since he entered his country's consulate in Istanbul on October 2, has been an outspoken critic of the ultra-conservative kingdom's government.
Separately on Sunday, the Arabic-language pro-government Saudi Arabian daily newspaper Okaz cited an unnamed official from the consulate in Istanbul as strongly denying the statements published by Reuters, quoting Turkish officials that Khashoggi had been killed in the mission in Istanbul.
Turkish authorities have concluded that the Saudi journalist had been killed at the consulate of Saudi Arabia in istanbul.
Khashoggi has been critical of some of Saudi Crown Prince Mohammed bin Salman's policies and Riyadh's intervention in the war in Yemen.
On Saturday, Trump said at a rally in West Virginia that although the Saudis "have got trillions of dollars", "we don't get what we should be getting" from them. In the kingdom's eyes, Khashoggi - through his platform in the Washington Post and access to stakeholders in the United States and Europe - was more than a critic: he had become a threat.
The Saudi source said that a security team including Saudi investigators had arrived in Istanbul on Saturday to take part in the investigation into Khashoggi's disappearance.
Khashoggi had asked for a document needed to remarry in Turkey, Tamimi said, and the consular staff "were surprised and said, yes, we will do it for you, but there is no time, and they agreed he will come back on Tuesday".
Turkish officials said Mr Khashoggi was killed on the premises and his body was then removed.
"Jamal was not killed and I do not believe he was killed", she wrote on Twitter, according to Reuters. It's there since 1744, I believe more than 30 years before the United States of America, And I believe, and I'm sorry if anyone misunderstands that, but I believe President (Barack) Obama, in his eight years, he worked against many of our agenda - not (only) in Saudi Arabia, but also in the Middle East.
Despite the intense interest concerning Khashoggi's whereabouts, little concrete evidence has emerged so far.
The Saudi government said it has begun intensive efforts to find its citizen, who has resided overseas for more than a year.
"His is a voice of reasoned criticism and wise comment that the Saudi crown prince should listen to", wrote Law, who said he had known Khashoggi for 16 years.
The prominent rights group also took global community to task for its "deafening silence on Saudi Arabia's crackdown on freedom of expression", adding that the worldwide community must demand an immediate explanation from Saudi Arabia's authorities about Jamal Khashoggi's fate or whereabouts.