The council made the request on Monday in reaction to Pyongyang’s latest missile test which was carried out on Saturday.
In a unanimously agreed statement the UNSC condemned the test, while stressing that the North show "sincere commitment to denuclearization through concrete action and stressed the importance of working to reduce tensions."
"To that end, the Security Council demanded the Democratic People's Republic of Korea conduct no further nuclear and ballistic missile tests," the council said.
It added that the council was prepared to issue further anti-North Korea sanctions.
North Korea launched an intermediate-range ballistic missile from the northwestern city of Kusong at around 5:30 a.m. (2030 GMT Saturday) and it flew 787 kilometers (489 miles) before landing in the sea between North Korea and Japan, the South Korean military said in a statement.