Hong also held a separate one-on-one meeting with National Security Advisor H.R. McMaster to discuss pending issues between the two countries, including nuclear and missile tensions with North Korea and the deployment of the US THAAD missile defense system.
The system was deployed earlier this month, days before South Korea elected Moon Jae-in, who had been critical of the system, its new president.
North Korea said the missile it had tested on Sunday was a "newly developed ballistic rocket" capable of carrying a large nuclear warhead.
Moon's apparent reluctance might be a result of South Korea's psychological warfare with China, which sees Thaad as a threat to its own military operations.
The two Koreas - technically still at war after the 1950-53 conflict ended only with a ceasefire instead of a peace treaty - have occasionally clashed along the border.
Abe and Moon Hee Sang, a heavyweight lawmaker of the ruling Democratic Party, also agreed to build a future-oriented bilateral relationship, with the Japanese leader noting Tokyo and Seoul are each other's "most important neighbors, sharing strategic interests" during the meeting in the prime minister's office in Tokyo.
A US Navy commander on Wednesday pushed for a "sense of urgency" over North Korea's nuclear and missile development, stressing that it even threatens Pyongyang's ally China and neighbour Russian Federation.
"We now need to apply pressure on North Korea, and Japan and the United States need to coordinate closely so as to apply pressure", Abe told reporters.
China retaliated against Seoul's deployment of the THAAD missile defense system by suspending visits to South Korea by Chinese tour groups and trips to China by South Korean entertainers. They said the North's "unacceptable" action underscored the importance of the U.S. -Japan alliance.
While experts insist that North Korea is still not capable of launching a missile that could reach the United States, the communist nation on Monday claimed it could.
Lee is in Beijing to deliver Moon's letter to Chinese President Xi Jinping and discuss summit talks.
Trump has said "a major, major conflict" with North Korea was possible and all options were on the table but wanted to resolve the crisis diplomatically and peacefully, possibly through the use of economic sanctions.
Haley said a plan is still in the works between the US, Japan, South Korea and China - North Korea's only major ostensible ally - to halt North Korea's progress on nuclear weapons and ballistic missiles.
Meanwhile, the top USA military officer in the Pacific described North Korea's recent military actions as "a recipe for a disaster" and warned against a sense of complacency in the face of increasing tensions on the Korean Peninsula.
Harris' comments came at a lecture for a Japanese think tank in Tokyo on Wednesday.
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