U.S. Secretary of State Rex Tillerson said Monday that the United Nations resolution on North Korea leaves no question in anyone’s mind that there is a common view on the matter.

In fact, Tillerson said that China and Russia’s support shows that the world expects them to help North Korea accept the realities of its situation. The recent resolution, he said, sends a strong message to all parties that they can have influence on North Korea.

The United Nations Security Council unanimously imposed new sanctions on North Korea on Saturday over its intercontinental ballistic missile tests in July. Reuters said the sanctions could slash the reclusive regime’s $3 billion annual export revenue by a third.

The U.S. official also said that, when conditions are right, it is possible to have a dialogue on the future of the North Korea issue.

The implementation and execution of the sanctions on Pyongyang will be carefully monitored, the secretary of state said. He added that the U.N. action sends a strong message that North Korea must understand the expectation of the international community.

This story is developing. Please check back for further updates.

—CNBC’s Saheli Roy Choudhury and Reuters contributed to this report.