"Police are likely to wield the greatest power among state institutions," Lee told a cabinet meeting on Tuesday, adding that the public questioned whether the force could bear the responsibility.
"Responsibility must be strengthened in proportion to the size of the authority."
Four people reported missing on Jeju were found dead over three days through Monday, authorities said.
The cases were unrelated, but two were alleged to have been closed by the same officer without confirmation that the missing people were safe.
The allegations have prompted police to review all 298 missing-person reports handled by the officer.
About 10 are being examined for possible improper closure, media reported.
One case involved Jang Mi-ran, a 37-year-old woman whose disappearance became a national controversy after police closed it without confirming her safety, according to the allegations. Her body was found on Monday, 104 days after she vanished.
The other involved a man in his 60s whose family reported him missing again, prompting a renewed search that ended with his body being found.
A court detained the officer on Tuesday on suspicion of dereliction of duty, falsifying official electronic records and obstructing official duties, the Yonhap News Agency reported.
The officer denied the charges and said he contacted the missing people, the report said, citing a police official.
Jeju, one of South Korea's most popular tourist destinations, drew 1.2 million foreign visitors in the first half of 2026, according to the Jeju Tourism Association.
Acting National Police Commissioner Yoo Jae-seong apologised and promised measures to prevent a recurrence.
Police have ordered supervisory sign-off for missing-person case closures pending an upgrade to their case-management system, Yoo told lawmakers on Monday.
"We will examine the entire system and make institutional improvements so that this never happens again," Yoo said, pledging to review all cases handled by the officer.
The National Police Agency placed four officers in the command line at the Jeju police station involved on administrative leave, Yonhap reported.
On Wednesday, Interior and Safety Minister Yun Ho-jung also apologised to the bereaved families and the public.
Yun and senior police officials stood and bowed in apology, pledging thorough measures to prevent a recurrence.
South Korean police received 70,814 reports of missing adults in 2025, official data showed.
More than 70,000 such reports have been filed annually since 2022, though the vast majority were solved within 30 days, police say.
