The new video broadcast by CNN, as well as a pro-government Turkish newspaper's report that a member of Crown Prince Mohammed bin Salman's entourage made four calls to the royal's office from the consulate around the same time, put more pressure on the kingdom.
Khashoggi, 59, vanished on October 2 after entering the Saudi mission to obtain documents for his wedding.
However, legal experts told Al Jazeera that the chances of extradition were slim.
William Schabas, professor of worldwide law at Middlesex University, said such a deal was unlikely.
Erdogan, who also said the issue of diplomatic immunity would also be discussed in regards to the case, was speaking at a meeting of his AK Party in parliament.
Turkey and the U.S. vowed on Tuesday to get to the bottom of the killing of Jamal Khashoggi and punish those responsible, after Saudi Arabia admitted that the prominent journalist died during a Saudi security operation in Istanbul.
Hariri, sitting beside the crown prince, even took part in the humour as the audience laughed.
The Turks claim to have audio recordings proving Mr Khashoggi was murdered by the Saudi hit squad, containing details of the grisly murder and dismemberment of the Wall Street Journal writer.
Significantly, President Trump yesterday broke with what had until that point been unequivocal support for Prince Mohammed, raising the possibility he could be implicated.
British Prime Minister Teresa May said Britain was "taking action against all suspects to prevent them entering the UK".
Trudeau says his government is looking at the contract with Saudi Arabia to see what can be done.
State media in Turkey said Wednesday that Saudi authorities had denied permission to Turkish police to search a well in the consulate's garden.
People around the world have been struck by the look on Salah's face as he shakes hands with MBS, as well as the presence of a bodyguard, who stands poised with a hand on his gun.
"Being a diplomat does not allow you to kill anybody. We are determined to punish those who are responsible for this murder".
"But there is an additional problem".
Softbank's $93bn Vision Fund to invest in tech firms was half-funded by Saudi Arabia's sovereign wealth fund. "Somebody really messed up", Trump said Tuesday.
Business leaders have been cancelling their scheduled trips to Riyadh amid the ongoing investigation into the death of Khashoggi, a USA resident and prominent critic of the Saudi government.
"The Saudi administration has taken an important step by admitting to the murder".
Following these arrests and dismissals, several organisations, including the United Nations and European Parliament, called for an independent investigation.