"They are now in the phase of working out what the best way to do that is," said a senior council diplomat, speaking on condition of anonymity. "It was left hanging that there clearly would be a military solution if needed."
The Trump administration is focusing its North Korea strategy on tougher economic sanctions, possibly including an oil embargo, a global ban on its airline, intercepting cargo ships and punishing Chinese banks doing business with Pyongyang, U.S. officials told Reuters earlier this month.
Washington is also stepping up pressure that began under the Obama administration against Cambodia, Laos and Malaysia, which have diplomatic and financial links to Pyongyang, to downgrade or cut diplomatic ties with North Korea.
The United States, which is president of the Security Council for April, urged members - in a note outlining Friday's meeting - to "show their resolve to respond to further provocations with significant new measures."
Diplomats say further provocations are considered a nuclear test or long-range missile launch.
U.S. State Department spokesman Mark Toner said Tillerson would on Friday push the international community to stand up to North Korea.
"Certainly, we've talked a lot about China's role ... that's a key aspect of this new strategy, is putting pressure on China, convincing China they need to do more, but this also needs to be a global effort," Toner told reporters.
U.N. Secretary-General Antonio Guterres is due to brief the Security Council on Friday, which will include foreign ministers from China, Britain and Japan. Tillerson is due to meet with his South Korean and Japanese counterparts before the council meeting and with his Chinese counterpart, Wang Yi, afterwards.
China has long promoted dialogue to resolve the "Korean nuclear issue," and the United States says it is open to talks, but they disagree over the sequence.
"The U.S. require (North Korea) to take some actual action to curtail their nuclear program, which could then be followed by talks, and the Chinese position is talks first, action later," the senior U.N. diplomat said.
Since 2006, North Korea has been subject to U.N. sanctions aimed at impeding the development of its nuclear and missile programs. The council has strengthened sanctions following each of North Korea's five nuclear tests.
Traditionally the United States and China have negotiated new sanctions before involving remaining council members. It took the council three months to act after the last nuclear test, in September, and diplomats said Washington appears to be laying the groundwork with China for faster negotiations next time.
Trump administration officials and Western diplomats say that Beijing is responding to increased pressure from Washington mostly because China has become frustrated with North Korea.
The Security Council has, however, also been split over what is fueling escalating tensions with North Korea. Western powers say Pyongyang's repeated nuclear and missile tests are purely to blame, while Russia and China also rebuke the United States for deploying an anti-missile defense system in South Korea.
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