The country first declared an emergency after suspecting someone in the city of Kaesong had COVID-19 in July. However, it has not been confirmed whether or not the case was a positive one or not.
North Korea claim the individual with the suspected case had illegally crossed the border into South Korea before returning back to the North.
Officially, North Korea says it has not had a single case of COVID-19.
If the Kaesong case is confirmed, it will be the first time the nation has openly admitted to having a positive case.
However, analysts have expressed doubt that this is really the case.
The news follows a meeting on Wednesday with senior North Korean officials, including Mr Kim.
In the meeting, supplies of food and financial aid were discussed, though a report by state news outlet the Korean Central News Agency did not specify exactly what measures were decided, PA said.
Kaesong has a population of around 200,000 people, and is located near to the border with South Korea.
When the city was put into lockdown last month, Mr Kim said it was a “critical situation in which the vicious virus could be said to have entered the country,” according to KCNA.
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According to Dr Edwin Salvador, the World Health Organisation’s representative to North Korea, the country had tested over 700 people as of the start of April.
He told Reuters: “As of 2 April, 709 people – 11 foreigners and 698 nationals – have been tested for COVID-19. There is no report of a COVID-19 case.”
Oliver Hotham, managing editor of North Korea news site NK News, told the BBC it is “very unlikely” the North has not had a single case due to the amount of trade that crosses the border between it and China.
He said: “I really don’t see how it’s possible they could have prevented it.
“But they really did take precautions early, so I think it’s possible they’ve prevented a full-on outbreak.”
Recently, foreign aid groups have said they have had to borrow money from the North Korean government in their efforts to help the country deal with the pandemic.
According to reports, international sanctions have blocked the delivery of medical supplies to the country.
The Red Cross said it managed to get medical supplies including a coronavirus diagnostics machine and 10,000 testing kits into North Korea in July after a lengthy delay.