SEOUL, South Korea — The North Korean leader Kim Jong-un, whose prolonged absence from public view generated speculation about his health and grip on power, has visited a housing project and was seen walking with a cane, according to the North’s state-run media on Tuesday.

The report was the first time the state-run news media had mentioned a public appearance by Mr. Kim since Sept. 3, when he was reported to have attended a concert. The report was likely to help dissipate the recent flurry of rumors over Mr. Kim’s whereabouts, many of which speculated on whether he had lost out in a power struggle inside the notoriously opaque government.

According to the Korean Central News Agency, Mr. Kim recently visited a district where his government had just finished a cluster of homes for satellite engineers. North Korea is particularly proud of its scientists who succeeded in putting a satellite into orbit on board a long-range rocket in December 2012. Washington considered the rocket program a cover for developing an intercontinental ballistic missile.

Mr. Kim “inspected various parts” of the housing district in Pyongyang, the news agency said, indicating that he had no trouble moving about. He expressed “great satisfaction” at the project and also posed for pictures with North Korean scientists who were to move into the new homes, the report added.