North Korea has rejected an offer of talks from the South as "insincere", in a rare meeting of high-level officials.Tensions have escalated on the Korean peninsula in recent months amid repeated missile tests by the North. The UN Security Council voted on Saturday to impose fresh sanctions.
South Korea proposed talks with the North last month, but Pyongyang has yet to officially respond.
South Korean media reported that Ms Kang and Mr Ri shook hands in a brief and unarranged meeting at an official dinner event held by the Association of Southeast Asian Nations (Asean).
A South Korean foreign ministry official confirmed the meeting to the BBC. However China, which is Pyongyang's closest ally, has disputed this account.
Foreign minister Wang Yi told journalists on Monday: "My feeling is that the North did not entirely reject the positive proposals raised by the South." He added that China also supported the South's initiatives.
All three countries' ministers are attending the Asean forum in Manila.