State Councilor Yang Jiechi, US Secretary of State Rex Tillerson and US Defense Secretary Jim Mattis co-hosted the meeting held at the US State Department.
General Fang Fenghui, chief of the People's Liberation Army's Joint Staff Department, was among the attendees.
Yang said the successful meeting between President Xi Jinping and President Donald Trump at Mar-a-Lago in April has charted the course for China-US relations in a new period, adding that under the consensus of the two leaders, the bilateral relations have made positive progress lately.
He called on both sides to maintain the positive direction to achieve more progress in the relationship.
The two sides agreed to make concerted efforts to expand mutually beneficial cooperation and manage and control their differences based on the principle of mutual respect.
Both sides hope to push forward relations onto a long-term and healthy development path, according to a press release from the Chinese delegation.
The two governments agreed on the importance of maintaining frequent high-level exchanges. They believe that with the joint efforts by both sides, the meeting between Xi and Trump at the G20 Summit in July in Hamburg, Germany, will achieve positive results, and the state visit to China later this year by Trump, at the invitation of Xi, will be a success.
They also expect a successful inaugural Comprehensive Economic Dialogue, Law Enforcement and Cybersecurity Dialogue, and Social and Cultural Issues Dialogue within this year. These dialogues, along with D&SD, form the new China-US Comprehensive Dialogue mechanism agreed to at Mar-a-Lago.
The Chinese side pointed out that the two sides should have a correct view of each other's strategic intention. China's strategic intention is clear. It is to defend its own sovereignty, security and development interest, according to the press release.
The US side expressed that it has recognized China's rapid and sustainable development and has no intention to contain or weaken China. Rather, it is willing to strengthen cooperation with China to develop a long-term and constructive relationship.
The US side also expressed that both countries should promote peace, stability and prosperity in the Asia-Pacific region by strengthening dialogue and cooperation.
The Chinese side spoke positively of the generally stable development of the military-to-military relationship. It called on both sides to elevate the relationship for more constructive, practical and effective cooperation.
Both sides also agreed that the defense chiefs of the two countries should exchange their visits at the earliest possible dates, plus a visit to China by the chairman of the US Joint Chiefs of Staff.
The Chinese side has stressed its principle on the issues relating to Taiwan and Tibet and the importance for the US side to keep its promise and properly handle both issues.
The Chinese side also reiterated its stance on the denuclearization of the Korean Peninsula by maintaining peace and stability and through talks and negotiations. China urged all sides to implement relevant UN Security Council resolutions and push for an early resumption of talks.
The Chinese side called for a serious consideration of China's "dual track" and "dual suspension" proposals. The "dual suspension" calls for the Democratic People's Republic of Korea to suspend its nuclear activities and for the US and South Korean side to suspend their large-scale military drills.
China has continued to urge a halt and cancellation of the deployment of the US THAAD missile defense system in South Korea.
The Chinese side reiterated China's undisputable sovereignty over the Nansha Islands and their surrounding waters.
China and US delegates also exchanged views on counterterrorism, Afghanistan and the Middle East.