CNN has no way of independently verifying the authenticity of the letter and has reported conflicting beliefs by various government officials on Kim's health condition in the past week.
The message was dated April 27, 2020, KCNA reported, as speculation mounted over Kim's health after he missed the celebration of his grandfather's birthday on April 15.
In the letter addressed to Ramaphosa, the North Korean leader expressed his certainty that the two nations' friendship would unendingly expand and develop, in addition to referencing Freedom Day, a public holiday celebrated in South Africa on Monday.
On Sunday, South Korean presidential adviser Moon Chung-in told CNN that the North Korean leader was 'alive and well' despite speculation about his wellbeing. The adviser to South Korean President Moon Jae-in said Kim had been staying in the Wonsan area on the country's east coast since April 13, adding: 'No suspicious movements have so far been detected.'
A website specializing in North Korean affairs published satellite images on Saturday that researchers said showed a train, 'probably belonging to Kim Jong Un,' which had been parked at a railway station serving Kim's luxurious Wonsan compound on the country's eastern coast since at least April 21.
According to 38 North, Kim's luxurious Wonsan complex includes leisure facilities such as nine large guesthouses, a recreation center, a protected port, a shooting range, a recreation building, a covered dock, and a small runway converted in 2019 into a horse-riding track.
Last week, a US official with direct knowledge told CNN the US was monitoring intelligence suggesting that Kim was in grave danger after surgery. Another US official told CNN on Monday that the concerns about Kim's health were credible, but the severity was hard to assess.
It followed a report by Daily NK, an online newspaper based in South Korea that focuses on North Korea, that Kim reportedly received a cardiovascular procedure because of 'excessive smoking, obesity, and overwork.' The news outlet said the leader was receiving treatment in a villa in Hyangsan County, north of Pyongyang.
After assessing that Kim's condition had improved, most of the medical team treating him returned to Pyongyang on April 19 while some of them remained to oversee his recovery, according to the news site. CNN was unable to independently confirm the report.
This is the fourth notice in the country's state media of routine state duties carried out by Kim since April 12 when reports first surfaced that Kim may be unwell.
On Sunday, North Korean state newspaper Rodong Sinmun said Kim sent thanks to workers who helped in remodeling the city of Samjiyon in North Korea. CNN could not independently confirm the authenticity of Sunday's report and whether the note of thanks came directly from the leader.
Though North Korea has not reported any cases within its borders -- a claim public health experts say is unlikely -- Pyongyang has taken the pandemic very seriously. The country quickly closed its borders to tourists and quarantined foreign diplomats, who eventually left. State media included several warnings and reports about the importance of proper hygiene in February, while also outlining steps the government was taking to combat the virus.