Last week brought the North's first acknowledgment of an "explosive" outbreak, with experts warning it could wreak devastation in a country with limited medical supplies and no vaccine programme.
Drugs procured by the state were not reaching people in a timely and accurate way, Kim told an emergency politburo meeting on Sunday, before visiting pharmacies near the capital's Taedong River, state news agency KCNA said.
Kim ordered immediate deployment of the "powerful forces" of the army's medical corps to "stabilise the supply of medicines in Pyongyang City," it added.
Although authorities had ordered distribution of national reserves of medicine, pharmacies were not well-equipped to perform their functions smoothly, Kim added, the agency said.
Among their shortcomings were a lack of adequate drug storage other than showcases, while salespeople were not equipped with the proper sanitary clothing and hygiene in their surroundings fell short of standards, the leader said.
He criticised the "irresponsible" work attitude, organisation and execution by the cabinet and the public health sector, it added.
Neighbouring South Korea will spare no effort to help the North fight its outbreak, President Yoon Suk-yeol told parliament on Monday, saying it was ready to provide COVID-19 vaccines and other medical support if Pyongyang agrees.
Seoul's unification ministry, responsible for relations between the neighbours, said it would soon propose a plan of support to the North.
North Korea's tally of the fever-stricken stood at 1,213,550, with 50 deaths by Sunday, after KCNA reported 392,920 more cases of fever, and eight more deaths. It did not say how many suspected infections had tested positive for COVID-19.
The North has blamed a large number of the deaths on people who were "careless in taking drugs" because of a lack of knowledge about the omicron variant of coronavirus and its correct treatment.