The United States expects China to persuade its ally North Korea to abandon its nuclear weapons and ballistic missile programmes, the White House has said, warning that the policy of “strategic patience” is over.

“We expect China to increase its role in persuading North Korea to move away from nuclear weapon and ballistic missile development and toward steps to create a better future for the North Korean people,” Press Secretary Sean Spicer told reporters.

The statement comes a day after President Donald Trump said that North Korean leader Kim Jong-Un was “acting very, very badly”, after Pyongyang conducted a ground test of a new type of high-thrust rocket engine on Saturday. The Korean Central News Agency called the test “a great event of historic significance” for North Korea’s indigenous rocket industry.

Mr. Trump’s remarks came as Secretary Rex Tillerson concluded his three-nation trip to Japan, South Korea and China, wherein North Korea’s “provocative” actions dominated his discussions.

Mr. Tillerson on Monday briefed Mr. Trump on his visit.

“This trip set the stage for future leader-level engagement between the US and China,” Mr. Spicer said.

“I think he sent a very clear signal that our policy of strategic patience is over. The President and the Secretary of State have an expectation that China employed multiple points of pressure on North Korea,” Mr. Spicer said.

“We know that, we don’t agree 100 per cent of the time with China, but as the State Department noted yesterday, both President Xi [Jinping] and Secretary Tillerson agreed that there are opportunities for greater cooperation between China and the US, and acknowledged that there are and will be in the future differences between the two countries,” he said.

Mr. Tillerson’s trip helped set them down that path.

“The follow-on meetings that the leaders intend to have will be helpful in that vein,” Mr. Spicer said.

The State Department, meanwhile, said Mr. Tillerson talked about the challenges of North Korea during his China visit.

“That was, frankly, a theme throughout his trip and how do we address it going forward; how do we address this threat going forward,” State Department acting spokesman Mark Toner told reporters.

Mr. Toner also said that the US is not backing away from its concerns about human rights in China. “With respect to other aspects of the relationship, we’re not walking away from our concerns about human rights, personal freedoms within China.”

“I think [Tillerson] also said during the trip that human rights is part and parcel in all of our conversations and in all of our discussions of the issues with respect to China, but with respect to other countries as well,” Mr. Toner said.