The prince is suspected by many, including US lawmakers, of ordering the killing of Jamal Khashoggi.
The Saudis have said that Khashoggi is dead but said the killing occurred after a fist fight went wrong and blamed a "rogue" operation.
Saudi Arabia's Foreign Ministry wrote on Twitter that the leaders shared "their deepest condolences and sympathy to the family of Jamal Khashoggi, may God rest his soul."
Commentators on Twitter pointed out that the family is unable to leave Saudi Arabia.
Karen Attiah, Khashoggi's editor at the Washington Post, has said that Saudi authorities imposed a travel ban to put pressure on the journalist's writing.
Turkish President Recep Tayyip Erdogan said evidence shows the journalist, who had four adult children, was "brutally murdered".
Erdogan said that a team including Saudi generals had flown in to carry out the mission.
The Saudi citizen had been a fierce critic of the leadership of Saudi Arabia, and in particular the Crown Prince.
He said the evidence collected so far shows Khashoggi was murdered in "a ferocious manner".
"To try and hide it would be an insult to humanity," Erdogan said in an address that was televised around the world. "Let's not forget that this building is within the borders of the Republic of Turkey."
He urged Saudi Arabia to reveal who ordered the "savage murder" at the kingdom's consulate in Istanbul and said the 18 Saudis suspected of carrying it out should be tried in Turkish courts.
Erdogan's comments contradicted Saudi accounts that Khashoggi died accidentally in a "fistfight" in the consulate — and for the first time the president also confirmed that a body double of Khashoggi was used as a decoy after he was killed.
However, he made no reference to any audio or video recordings, something that would be seriously damaging to the Saudi government.
He did not mention the Crown Prince, who some US politicians have speculated ordered the murder — but did speak of King Salman's "sincerity" in the inquiry so far.
Mr Erdogan vowed Turkey would continue in its pursuit of the truth.
"From the person who gave the order, to the person who carried it out, they must all be brought to account."
He demanded Saudi Arabia reveal who helped the killers - someone he called a "local cooperator" — who supposedly took Khashoggi's remains away.
