The North Korean leader gave "field guidance" to a newly built residential district and visited the Natural Energy Institute of the State Academy of Sciences, state news agency KCNA reported Tuesday.
Kim hadn't been seen in public since he reportedly attended a concert with his wife on September 3. It's his longest absence from official events since he made his first public appearance in 2010, according to NK News, a website devoted to analyzing North Korea.
In the undated photos, Kim was surrounded by officials and could be seen walking with a cane. He was smiling and didn't appear, in the photos at least, to be in pain.
Before his disappearance, Kim was seen limping, prompting theories that he was suffering everything from weight gain to gout.
His sudden disappearance took a concerning turn on Friday
when he didn't appear at a events to mark the 65th anniversary of the Worker's Party of North Korea.
In previous years, Kim has attended the Kamsusan Palace of the Sun in Pyongyang to pay tribute to his father and grandfather. This year his name was absent from the list of attendees. Instead, KCNA reported that flowers were presented at the shrine in Kim's name.
Kim's failure to appear fueled rampant speculation: Was there a power shift in the North Korean hierarchy? Could the young leader be ill?
According to Dr. Kim So-Yeon, the former personal doctor to Kim's grandfather Kim Il Sung, Kim inherited a number of health issues, including psychological problems and a history of obesity.
She told CNN both Kim Il Sung and Kim's father Kim Jong Il suffered from diabetes, heart problems and stress.
After studying the photos, she said Kim's face appeared to have been swollen due to painkillers. And she also speculated that he has been receiving hormone shots to make him look more like his grandfather, the much-revered founder of North Korea.
On Tuesday, U.S. National Security Council spokesman Patrick Ventrell said he could not confirm the KCNA report.
"We have seen these breaking reports but have nothing for you on their authenticity at this time," he said.
Before this absence, Kim's longest disappearance from public view as Supreme Leader was 24 days between June 7 and July 1, 2012. His second longest absence was for 29 days between July 28 and August 27, 2011 -- while his father was still alive, NK News said.
Kim's sole public appearance in September was at a Moranbong Band concert at Pyongyang's Mansudae Art Theatre, reported by state media on September 4.
He was accompanied by his wife, Ri Sol Ju, his sister Kim Yo Jong and several top officials including Hwang Pyong So.