U.S. military sales to Saudi Arabia have come under increased scrutiny over the Saudi-led coalition's war in Yemen.
When asked about fears that Saudi Arabia could use the S-400 system against Iran, a Russian ally, Peskov said Moscow's decision to offer the missiles to Riyadh was not aimed at any third party.
"We can speak only for ourselves", said Peskov.
The approval opens the way for Saudi Arabia to purchase 44 Terminal High Altitude Area Defence (THAAD) launchers and 360 missiles, as well as fire control stations and radars.
The king has been visiting Russian President Vladimir Putin in talks over oil and Syria, Saudi's al Arabiya television reported.
The US sale has not yet "concluded", it confirmed.
The S-400 is Russia's most advanced long-range anti-aircraft missile system and can carry three types of missiles capable of destroying targets, including ballistic and cruise missiles.
The following day, the U.S. Defense Security Cooperation Agency announced $15 billion in weapons sales to Riyadh.
Saudi Arabia and the United States are highly critical of what they consider Iran's aggressive behaviour in the Middle East.
"This potential sale will substantially increase Saudi Arabia's capability to defend itself against the growing ballistic missile threat in the region". "This visit is the beginning of strategic cooperation", al Harithi said.
Its recent deployment by the US military in South Korea to protect against any North Korean strike drew protests from Beijing, who feared its sensors would be able to penetrate into Chinese air space and upset the balance of power. Saudi Arabia's neighbours, Qatar and the United Arab Emirates, have also been supplied THAAD systems.