The council also said it was taking seriously the two countries' discussions on military cooperation, including the development of intercontinental ballistic missiles (ICBM).
While urging Pyongyang and Moscow not to trade weapons, South Korea will work with the United States, Japan and the international community to deal with the situation, the council said in a statement.
"The government said that with any actions that threaten our security by North Korea and Russia violating (U.N.) Security Council resolutions, there will be a price to pay," it said.
The message comes after the NSC held a meeting to discuss the summit between North Korean leader Kim Jong Un and Russian President Vladimir Putin.
The South Korean meeting was attended by senior officials including the foreign minister as well as the unification minister, who is in charge of relations with North Korea.
Earlier, Unification Minister Kim Young-ho also expressed concern over military cooperation between North Korea and Russia.
(Reporting by Hyunsu Yim; Editing by Kevin Liffey and Angus MacSwan)

Russian President Vladimir Putin (R) shakes hands with North Korean leader Kim Jong Un (L) during their meeting on the Vostochny cosmodrome outside of the town of Tsiolkovsky (former Uglegorsk), some 180 km north of Blagoveschensk in Amur region, Russia, 13 September 2023. EPA-EFE/VLADIMIR SMIRNOV/SPUTNIK/KREMLIN POOL