Washington Post contributor Jamal Khashoggi, 59, vanished after an appointment with Saudi officials on Tuesday.
A Turkish government source told AFP that police believed Khashoggi was killed at the Istanbul consulate, which Riyadh strongly denied.
Khashoggi had gone to the consulate to obtain documents needed to marry his Turkish fiancee.
Erdogan said he would wait for the outcome of the current investigation before taking a decision.
"I am following the (issue) and we will inform the world whatever the outcome" of the official probe, the president told reporters in Ankara.
Protesters hold pictures of Saudi Journalist Jamal Khashoggi during a demonstration organized by Turkish-Arabic Media Association. Source: AAP
"We hope to have results very quickly," he added. "I am waiting, with high hopes."
He said police were examining CCTV footage of entrances and exits at the consulate and Istanbul airport.
Police said earlier that around 15 Saudis, including officials, arrived in Istanbul on two flights on Tuesday and were at the consulate at the same time as Khashoggi.
"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 told AFP on Saturday.
The journalist went to the building but "did not come back out", police were quoted as saying by Turkey's state-run Anadolu news agency.
'Baseless claims'
Saudi Arabia has denied the reports.
A statement on Sunday by the state-run Saudi Press Agency (SPA) cited a diplomatic officer who categorically denied "these baseless allegations, and expressed his doubt that they came from Turkish officials that are informed of the investigation or are authorised to comment on the issue".
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".
The journalist's fiancee, Hatice Cengiz, said on Twitter she was "waiting for an official confirmation from the Turkish government" before she could believe the claims.
Khashoggi has been critical of some of Saudi Crown Prince Mohammed bin Salman's policies and Riyadh's intervention in the war in Yemen.
His criticisms appeared in both the Arab and Western press.
The former government adviser, who turns 60 on October 13, has lived in the United States since last year to avoid possible arrest.
Yasin Aktay, an official in Turkey's ruling Justice and Development Party (AKP) who was close to the journalist, said Khashoggi had made an appointment in advance with the consulate and called to check the documents were ready.
"His friends had warned him, 'Don't go there, it is not safe,' but he said they could not do anything to him in Turkey," said Aktay.
He added that he still hoped the reports of his friend's death were untrue.
