Wang Yi also said he was concerned by a possible U.S. deployment of its sophisticated THAAD (Terminal High Altitude Area Defense) missile defence system to South Korea, saying it could also be used to target China.
North Korea has been under U.N. sanctions since its first nuclear test in 2006. It has conducted three more atomic tests since then, including last month's, and numerous ballistic missile launches.
Washington and Beijing have appeared divided over how to respond to North Korea, with Washington urging tougher sanctions and Beijing stressing the need for dialogue.
However, Wang said in Munich that it was time for a "strong" resolution covering a wide range of areas.
"(We) support the United Nations Security Council to take further steps and in adopting a new resolution so that North Korea will pay the necessary price and show there are consequences for its behaviour," the minister said, speaking through an interpreter.
China has insisted it is already making great efforts to achieve denuclearisation on the "Korean peninsula" and has previously rejected any "groundless speculation" on its North Korea stance, following remarks from U.S. officials that China could do more.
The U.N. Security Council is discussing a new resolution. Diplomats say the Americans have been pushing for tough measures that go beyond targeting North Korea's atomic weapons and missile programs, while China wanted any future steps to focus on the question of nonproliferation.