Speaking before a dinner with Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in in Hamburg in the wake of North Korea’s long-range ballistic missile test this week, Mr Trump on Thursday said “never give up” when asked whether he no longer placed any faith in the Chinese leader.

The comments appeared to contradict previous remarks where he said China had failed to put sufficient pressure on North Korea to change the direction of Kim Jong Un’s regime, which has conducted regular missile tests and this week demonstrated the potential capability to strike Alaska. Before leaving Washington for Poland and Hamburg, Mr Trump tweeted: “Trade between China and North Korea grew almost 40% in the first quarter. So much for China working with us — but we had to give it a try!”

US-China relations entered a more co-operative phase earlier this year after Mr Trump hosted Mr Xi in Florida, and later described his Chinese counterpart as a “great guy” who would persuade Mr Kim to abandon his missile and nuclear programmes.

While US officials concede that China has increased its pressure on North Korea, they are frustrated that Beijing has balked at doing more — concerns exacerbated by North Korea’s intercontinental ballistic missile launch.

Over the past week, the US has taken punitive measures against China, including sanctioning two Chinese individuals and notifying a Chinese bank that it would be unable to access the US financial system because of accusations that the institution was helping North Korea to launder money. Mr Trump also agreed a $1.4bn arms sales package to Taiwan — a move that angered China, which claims the island as part of its territory.

North Korea is expected to be high on the agenda when Mr Trump meets the other G20 leaders in Hamburg, and particularly when he meets Russia’s President Vladimir Putin on Friday and Mr Xi the following day. China and Russia have expressed concern at some of the language coming from America, which has created the impression that the US is edging closer to taking military action.

“We are at a pivot point. If Xi agrees to up the pressure on North Korea, US-China ties will be back on track and Trump will give China a better trade deal. From Trump’s perspective, the ball is in Xi’s court,” said Bonnie Glaser, a China expert at the Center for Strategic and International Studies in Washington. “There is a positive path forward that serves both countries interests. Xi might want to buy time at least until after the 19th Party Congress (later this year).”

James Mattis, US defence secretary, said on Thursday that the latest North Korean test did not bring the US closer to war. His comments came a day after Nikki Haley, US ambassador to the UN, said the diplomatic path was narrowing and the US would use military force if there was no other choice.

“I do not believe this capability in itself brings us close to war because the president’s been very clear, and secretary of state’s been very clear that we are leading with diplomatic and economic efforts,” said Mr Mattis.

Speaking in Poland before he flew to Hamburg, Mr Trump warned that he was considering “severe” actions in response to North Korea. Mr Mattis said the US was working with the Chinese to tackle the problem, but added: “Any kind of effort by North Korea to start a war would lead to severe consequences.”