Russian President Vladimir Putin and Saudi King Salman bin Abdulaziz held a phone talk on Thursday evening, a statement by the Kremlin said.
The two leaders discussed the killing of journalist Jamal Khashoggi in the Saudi Consulate in Istanbul and the situation in Syria, the statement said.
The king assured Putin that the Saudi government was determined to hold the guilty parties accountable and to make sure "they receive their punishment".
They also discussed the situation in Syria and questions related to mutual cooperation between Russia and Saudi Arabia, including energy sector.
The talk was initiated by the Saudi side, it added.
During their conversation, the Saudi king also invited Putin to visit his country, the statement said.
Khashoggi, a Washington Post columnist and vocal critic of the crown prince, was last seen entering the Saudi consulate in Istanbul on Oct. 2.
Khashoggi's death was described as "murder" for the first time by Saudi Foreign Minister Adel al-Jubeir on Sunday.
Riyadh had initially denied that Saudi officials had any knowledge of what had happened to the 59-year-old dissident journalist, saying he had left the consulate after picking up papers for his forthcoming marriage.
The kingdom admitted on Saturday - 18 days after the incident - that Khashoggi indeed died in the consulate but blamed the death on a "fistfight" and said more than a dozen people were being questioned.
On Thursday, a Saudi public prosecutor said the killing was premeditated, citing the Turkish-Saudi joint probe, Saudi media said.