The two sides' exchanges have ground nearly to a halt after the North closed borders and temporarily shut a joint liaison office in a border city to avert an outbreak, while the South added 438 infections on Thursday to swell its tally to 5,766.
In the letter delivered on Wednesday, Kim voiced concern over Moon's health, and expounded what he described as his "honest view and position" regarding the situation on the Korean peninsula, Moon's office said, without elaborating.
"Chairman Kim wished to console our citizens who are fighting the coronavirus," Yoon Do-han, Moon's senior press secretary, told reporters.
"He said he believes we will win, and hoped the health of southern compatriots will be protected."
Moon responded with a letter of thanks, Yoon added.
The rare message came less than two days after Kim's sister, Yo Jong, issued a statement attacking Moon's office for criticising a military drill by the North.
North Korea had resumed missile testing on Monday after a three-month pause, prompting Moon's office to urge a halt.
Kim Yo Jong, who is also a senior official of the North's ruling party, said the exercise was not meant to threaten anyone, deriding Seoul for what she called "perfectly foolish" words and acts.
North Korea has not confirmed any virus infections, but state media said people showing symptoms faced a month in quarantine, while further "high-intensity" measures included stricter checks in border areas, at airports and sea ports.
Moon offered to help the North's prevention efforts, but Pyongyang has not responded, officials said.
France's foreign ministry spokeswoman Agnes von der Muhll told reporters on Thursday that Paris was closing its cooperation bureau in Pyongyang as a result of North Korea's measures and advised against all travel to the country.
"North Korea has taken drastic containment measures since the end of January, which target foreign representations in particular and seriously hamper the proper functioning of the French Cooperation Office in Pyongyang." she said.
"In these conditions, in conjunction with our European partners, it was decided to temporarily close the French Cooperation Office, until these measures are relaxed."
The reclusive communist state has no official diplomatic relations with France, one of only two European Union countries along with Estonia to cut ties with North Korea until it abandons its nuclear weapons program and improves its human rights record.
