The United States and China agreed Wednesday that companies of the two countries should not conduct business with U.N.-sanctioned North Korean entities as part of increased pressure on Pyongyang to curb its "illegal" nuclear and missile programs.

"We reaffirmed our commitment to implement in full all relevant U.N. Security Council resolutions," U.S. Secretary of State Rex Tillerson told reporters after an inaugural high-level security meeting with senior Chinese officials in Washington.

"For example, we both agreed that our companies should not do business with any U.N.-designated North Korean entities in accordance with these resolutions," he said.

Citing money laundering, malicious cyber activity and the extortion of North Korean laborers, Tillerson said North Korean leader Kim Jong Un's regime has engaged in "a number of criminal enterprises that help fund its weapons programs," and urged China to "step up our efforts to help to curtail these sources of revenue."

"Countries around the world and the U.N. Security Council are joining in this effort, and we hope China will do their part as well," the top U.S. diplomat said.

The United States has been pushing China to tighten sanctions on North Korea, believing that Beijing -- by far the largest trading partner of Pyongyang and a major oil supplier to the country -- has not fully exerted its influence and economic leverage over North Korea to change its provocative behavior.

During Wednesday's talks, the United States "reiterated to China that they have a diplomatic responsibility to exert much greater economic and diplomatic pressure on the (North Korean) regime if they want to prevent further escalation in the region," Tillerson said.

In the first round of the U.S.-China Diplomatic and Security Dialogue, Tillerson and Defense Secretary Jim Mattis hosted State Councilor Yang Jiechi, China's top foreign policy official, and Gen. Fang Fenghui, chief of the Joint Staff Department of the People's Liberation Army.

The nuclear and missile threat posed by North Korea was a top priority in the talks, a new framework launched by U.S. President Donald Trump and Chinese President Xi Jinping at their meeting in Florida in April.

North Korea has conducted five nuclear tests and appears to have made progress in developing a nuclear-tipped intercontinental ballistic missile that could strike as far as the U.S. mainland.

Mattis said after the meeting that the two sides "affirmed our strong commitment to cooperate, including through the U.N., to realize our shared goal of denuclearization of the Korean Peninsula."

Signaling U.S. frustration over China's perceived reluctance to further tighten the economic screws on North Korea, Trump wrote in a tweet Tuesday, "While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out. At least I know China tried!"

Trump has told Xi that the United States will impose sanctions on Chinese companies with links to North Korea's nuclear and missile development if Beijing fails to crack down on such entities, Tillerson said at a congressional hearing last week.

The United States has provided China with a list of entities Washington believes Beijing needs to take action against, he said.

Wednesday's talks came amid rising calls in the United States for tougher sanctions on North Korea after the death Monday of Otto Warmbier, an American university student released by the country last week in a coma after more than 17 months' imprisonment for what Pyongyang said was an attempt to steal an item bearing a propaganda slogan.

"There's no way that we can look at a situation like this with any kind of understanding," Mattis said. "This goes beyond any kind of understanding of law and order, of humanity, of responsibility towards any human being."

Turning to competing territorial claims between China and its smaller neighbors such as the Philippines and Vietnam in the South China Sea, Tillerson indicated the United States told China to stop its island building and militarization of outposts in disputed areas of the sea.

"We oppose changes to the status quo of the past through the militarization of outposts in the South China Sea and excessive maritime claims unsupported by international law," he said, in a veiled criticism of Beijing's unilateral claim of almost the whole of the sea.

Among other issues, the two sides agreed to increase coordination in the global fight against terrorism and Islamic State extremists, as well as to step up risk-reduction efforts between the two armed forces and exchange of officers to improve transparency and mutual understanding, according to Mattis.