The KCNA agency said on Tuesday that Mr Kim "gave field guidance" at a newly-built scientists` residential district.
Rodong Sinmun daily newspaper carried several photographs of Mr Kim using a walking stick as he inspected the site.
The absence of the 32-year-old leader has prompted a flurry of speculation about his health.
Some have even questioned if he remains in control of the state.
Official media have cited unspecified personal "discomfort" as grounds for Mr Kim`s absence from public view.
On Sunday, North Korea`s ambassador to London told the BBC that Mr Kim was in good health.
The desire of state-run media to end speculation about Mr Kim also indicates he has not been the victim of a coup, says the BBC`s Steve Evans in the South Korean capital, Seoul.
KCNA said that Mr Kim was briefed on the Wisong Scientists Residential District "before a map showing its bird`s-eye view" and that he then "overlooked it".
"Looking over the exterior of the apartment houses and public buildings, decorated with diverse coloured tiles, (Mr Kim) expressed great satisfaction, saying they looked very beautiful," the agency said.
It also said that Mr Kim visited the newly-built Natural Energy Institute of the State Academy of Sciences.
Although the news release was dated Tuesday, it did not specify on which day he made the visits.
During his absence, Mr Kim missed two high-profile public events - the 10 October anniversary of the establishment of the Korean Worker`s Party and the 9 September Foundation Day of the North Korean State.
Analysts said they were two days in the political calendar when the leader would be expected to make an appearance.
Kim Jong-un took office on the death of his father, Kim Jong-il, in December 2011 and was quickly named head of the party, state and army.
In 2012 he was appointed marshal - the highest military rank - following a high-level military reshuffle.
Then, in December 2013, Mr Kim purged and executed his uncle, Chang Song-thaek, who state media said had been plotting a coup.