Lee said later on Monday that he had not decided whether to accept Kang's resignation.
Kang offered to resign in order to take "overall responsibility" as the president's top aide after Lee acknowledged at a press conference last week that public concern over his administration reflected his own shortcomings, Yonhap News Agency reported, citing a presidential official.
The resignation follows criticism over recent government appointments, including the withdrawal of the nominations of former gender equality and family minister nominee Yong Hye-in and former justice minister nominee Kim Seung-won.
Lee's approval rating rose 1 percentage point to 34.8% in a survey released on Monday by pollster Realmeter, marking its first increase in 10 weeks.
(Reporting by Joyce Lee and Heejin KimEditing by Ed Davies)

South Korean Prime Minister Han Seong-sook (L), ruling Democratic Party leader Kim Min-seok (C), and presidential chief of staff Kang Hoon-sik (R) attend a consultative meeting of senior party and government officials at the prime minister's residence in Seoul, South Korea, 23 August 2026. EPA/YONHAP SOUTH KOREA OUT
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