The Democratic People's Republic of Korea (DPRK) on Sunday warned the South to stop crossing into its territorial waters as ships search for the body of a Seoul official shot dead at sea by Pyongyang's soldiers.

The fisheries official was shot dead by DPRK troops on Tuesday, prompting a rare public apology from leader Kim Jong Un.

Seoul's military has accused the DPRK's soldiers of pouring oil over the man's body and burning it after shooting him. Pyongyang has denied it, saying it had burned the floating device that the man was on, not his body.

Read more: DPRK expresses regrets over killing of ROK official

The death was an "awful case which should not have happened," the official KCNA news agency said on Sunday, adding that Pyongyang was organizing a search operation in its waters to help locate the body.

It said the country was considering "procedures and ways of handing over any tide-brought corpse to the south side ... in case we find it during the operation."

But it warned that South Korean vessels near the site of the incident had crossed into the DPRK's waters.

"We can never overlook any intrusion into our territorial waters and we seriously warn the south side against it," KCNA said.

"It arouses our due vigilance as it may lead to another awful incident."

South Korean President Moon Jae-in convened an emergency meeting with his security ministers on Sunday and said Seoul had requested a joint probe with the North on the shooting.

"The North's swift apology and its promise to prevent a recurrence were assessed positively," Moon's office said in a statement.

Apologies from Pyongyang are unusual and the message from Kim came with inter-Korean ties in a deep freeze and nuclear negotiations between Pyongyang and Washington deadlocked.

(With input from Reuters and AFP)