BEIJING (Reuters) - China and the United States agreed that efforts to denuclearize the Korean Peninsula should be “complete, verifiable and irreversible”, Chinese state media said on Saturday, reporting the results of high level talks in Washington this week.

“Both sides reaffirm that they will strive for the complete, verifiable and irreversible denuclearization of the Korean Peninsula,” a consensus document released by the official Xinhua news agency said.

U.S. Secretary of State Rex Tillerson had said on Thursday that the United States pressed China to ramp up economic and political pressure on North Korea, during his meeting with top Chinese diplomats and defense chiefs.

China’s top diplomat Yang Jiechi and General Fang Fenghui met Tillerson and Defense Secretary Jim Mattis during the talks. Yang later met with U.S. President Donald Trump in the White House, where they also discussed North Korea, Xinhua reported.

The consensus document also highlighted the need to fully and strictly hold to U.N. Security Council resolutions and push for dialogue and negotiation, which has long been China’s position on the issue.

Military-to-military exchanges should also be upgraded and mechanisms of notification established in order to cut the risks of “judgment errors” between the Chinese and U.S. militaries, the statement also said.

Chinese state media described the talks, the first of their kind with the Trump administration, as an upgrade in dialogue mechanisms between China and the United States, following on from President Xi Jiping’s meeting with Trump in Florida in April.

Xi and Trump are next expected to meet again in Hamburg during the G20 Summit next month.

A day last week’s talks, President Donald Trump said China’s efforts to use its leverage with North Korea had failed, raising fresh doubts about his administration’s strategy for countering the threat from North Korea.

The death of American university student Otto Warmbier earlier this week, after his release from 17 months of imprisonment in Pyongyang, further complicated Trump’s approach to North Korea.

China, North Korea’s main trading partner, has been accused of not fully enforcing existing U.N. sanctions on its neighbor, and has resisted some tougher measures.

Washington has considered further “secondary sanctions” against Chinese banks and other firms doing business with North Korea, which China opposes.