The Trump administration had sought a full United Nations embargo on oil exports to North Korea, among other harsh measures, but China made clear it disagreed.
"I think it's clear that with respect to oil and a complete embargo on oil from the U.N. Security Council, that's going to be very hard", Tillerson added, according to an official transcript.
U.S. Secretary of State Rex Tillerson said in a meeting with U.K. Prime Minister Theresa May late Thursday that Myanmarese violence against the Rohingya Muslims is "unacceptable" and called for a solution.
These continued provocations only deepen North Korea's diplomatic and economic isolation, he added. China holds veto power as a permanent member of the U.N. Security Council.
Last month, North Korea fired another ballistic missile from a similar area near the capital that flew over Hokkaido before splashing down into the ocean, as well.
He cautioned against pursuing alternative efforts at engagement with Pyongyang - a possible reference to comments this week by German Chancellor Angela Merkel who offered to act as a facilitator, if needed, in diplomacy.
The aim of the meeting - attended by the UN envoy for Libya Ghassan Salamé and representatives from France, Italy, Egypt and the United Arab Emirates - is to "discuss how to break the political deadlock in Libya", Britain's foreign ministry said. Today it is split between rival parliaments and governments in the east and west, each backed by a set of militias, tribes and political factions.
"Helping to bring stability to Libya is a vital part of United Kingdom efforts to tackle the threat from terrorism and the issue of illegal migration, which exist in close proximity to Europe", the Foreign Office said.
Tillerson also suggested US would push forward with additional unilateral sanctions against the regime.