President Donald Trump (L) and China's President Xi Jinping walk along the front patio of the Mar-a-Lago estate after a bilateral meeting in Palm Beach, Florida, April 7, 2017.

The United States pressed China to exert more economic and diplomatic pressure on North Korea to help rein in its nuclear and missile programs during a round of high-level talks in Washington on Wednesday.

The meeting of top U.S. and Chinese diplomats and defense chiefs was held a day after President Donald Trump said China's efforts to use its leverage with Pyongyang 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 this week, after his release from 17 months of imprisonment in Pyongyang, has further complicated Trump's approach to North Korea, his top national security challenge.

"We reiterated to China that they have a diplomatic responsibility to exert much greater economic and diplomatic pressure on the regime if they want to prevent further escalation in the region," U.S. Secretary of State Rex Tillerson told reporters at a joint news conference with Defense Secretary Jim Mattis.

Mattis vowed to "continue to take necessary measures to defend ourselves and our allies" against North Korea, which is working to develop a nuclear-tipped missile capable of hitting the United States.

But with the long-standing option of pre-emptive military strikes seen as far too risky for now, Trump's aides are stressing economic and diplomatic pressure.

Tillerson said Trump would make a state visit to China this year, and Mattis said both sides agreed to expand military-to-military ties, signaling the new administration's determination to continue efforts to improve relations between the world's two largest economies, despite frustration over North Korea.

North Korea topped the agenda at the newly established Diplomatic and Security Dialogue, which paired Tillerson and Mattis with Chinese State Councilor Yang Jiechi and General Fang Fenghui, chief of joint staff of the People's Liberation Army.

While the U.S. officials stressed agreement on the goal of North Korean denuclearization, the talks also dealt with China's sweeping territorial claims in the South China Sea, with the Americans reaffirming opposition to Beijing's militarization of islands it is building in the strategic waterway.