The approval, announced on October 6, clears the way for Saudi Arabia to purchase 44 Terminal High Altitude Area Defense launchers and 360 interceptor missiles, as well as fire control stations, radars and trucks.
"We can speak only for ourselves", said Peskov.
"THAAD's exo-atmospheric, hit-to-kill capability will add an upper-tier to Saudi Arabia's layered missile defense architecture".
The king has been visiting Russian President Vladimir Putin in talks over oil and Syria, Saudi's al Arabiya television reported.
It is expected the sale will beef-up security in the nuclear-hungry Middle East. US Congress has 30 days to object.
According to the Russian Kommersant newspaper, an agreement has already been reached on a $3-billion deal to supply the Saudis with Russia's most advanced air defense missile system, the S400 Triumph.
The State Department said it would advise Congress that, in Saudi hands, the system would act to stabilize the situation in the Gulf and help defend USA forces in the region and their allies, who face a growing Iranian missile capability.
"This proposed sale will support the foreign policy and national security objectives of the United States by improving the security of a friendly country", the statement read.
Both Washington and Saudi Arabia accuse Tehran of aggressive and disruptive behavior in the region.
Last week, Australia said it will outfit its new naval warships with Lockheed's Aegis air-defense system, which is also used by the US and Japan and would help the three navies coordinate on missile-defense missions. Saudi Arabia's neighbours, Qatar and the United Arab Emirates, have also been supplied THAAD systems.
Earlier, Saudi Arabia concluded a deal worth billions of dollars with the USA.