Esper made the remark at the start of talks with South Korean Defence Minister Jeong Kyeong-doo, reports Yonhap News Agency.
The US "will remain resolute in the enforcement of the UN Security Council resolutions until the North engages in the complete, verifiable, irreversible denuclearization of the Korean Peninsula", Esper said.
"As President (Donald) Trump has made clear, the US is willing to engage diplomatically with North Korea to make progress on all commitments made in the Singapore joint statement to achieve those ends," he said.
Calling the Indo-Pacific region the US' priority, Esper noted that his visit to South Korea is to reaffirm the "ironclad" alliance, which is "the linchpin of peace and security" on the Korean Peninsula and the Northeast Asia.
Esper arrived in South Korea on Thursday for a two-day visit on the final leg of his five-nation trip to the Asia-Pacific region, which also took him to Australia, New Zealand, Japan and Mongolia, Yonhap reported.
During Friday's talks, the two sides were expected to share their assessment of the security situation on the Korean Peninsula and discuss major pending issues, including how to boost cooperation for the denuclearization of North Korea and the envisioned transfer of the wartime operational control (OPCON) from Washington to Seoul, according to South Korea's Defence Ministry.
The meeting comes after North Korea intensifying its display of weapons in recent weeks by test-firing newly developed short-range ballistic missiles several times, saying the launches were to send warnings against the combined military exercise between South Korea and the US.
( With inputs from IANS )