The meeting took place in Cebu, where both ministers are attending the 13th ASEAN Defense Ministers' Meeting-Plus (ADMM-Plus), scheduled for Thursday.
South Korea's defense ministry released photographs of the two ministers meeting and shaking hands, marking their first face-to-face encounter since Kang took office on September 22.
Details of their discussions have yet to be disclosed, but the two were expected to address major alliance issues, particularly the OPCON transition and preparations for the annual Security Consultative Meeting (SCM).
Seoul is seeking to complete the verification of the Future Combined Forces Command's full operational capability (FOC) this year and establish a target year for the OPCON transfer.
FOC verification is the second stage of a three-phase, conditions-based process designed to assess South Korea's ability to lead combined forces after wartime command authority is transferred from Washington.
However, differences remain over whether the necessary conditions have been met.
South Korea wants to complete the transition during President Lee Jae Myung's term, which ends in 2030, while Washington has emphasized that the transfer must be based on military readiness rather than a political timetable.
The disagreement has complicated preparations for the SCM, which is usually held in late October or early November.
Although the meeting had been expected to take place in December, speculation is growing that it could be postponed until early next year.
Related military consultations, including the Permanent Military Committee (PMC) and Military Committee Meeting (MCM), have also faced delays.
Before departing for the Philippines on Tuesday, Kang acknowledged that the OPCON issue would likely be discussed.
"We will basically discuss alliance issues, and I expect the OPCON transition will naturally come up," Kang told reporters, adding that he would consult closely with his U.S. counterpart.
The ministers may also have addressed other defense priorities, including South Korea's plans to develop nuclear-powered submarines and broader efforts to strengthen bilateral military cooperation.
Kang's visit marks his first appearance at a major multilateral defense meeting since taking office.
He is also expected to hold bilateral talks with counterparts from Japan and other regional countries to discuss expanding defense exchanges and defense industry cooperation.
At Thursday's ADMM-Plus plenary session, Kang is expected to outline Seoul's efforts to promote peace on the Korean Peninsula and emphasize the importance of regional security cooperation.
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