Pyongyang's footballers will compete in both men's and women's events during the Asian Games, which will run from September 19 to October 4, the North's official Korean Central News Agency said in a brief article.
South Korea has invited North Korea to participate in the so-called Asiad games through the Olympic Council of Asia, a body that controls all sports in Asia. But there has been no official reply yet from the North.
"We welcome North Korea's participation in the football event and hope it will also take part in other events," Song Young-Gil, the mayor of Incheon, said in a statement quoted by Yonhap news agency.
Cross-border ties are currently in a state of watchful limbo, with both sides voicing willingness to improve relations while accusing the other of lacking sincerity.
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Earlier this month, Park had called for the resumption of reunions for families separated by the Korean War. But the North rejected the proposal, citing the South-US exercises as a major barrier.
The North also renewed demanded South Korea scrap its planned joint military drills with the United States, an exercise which Pyongyang routinely condemns as a provocative rehearsal for an invasion.
But South Korea has reacted negatively to the North's proposal, saying it would not cancel its military drills with the US.
Last year's exercises were held following North Korea's third and largest nuclear test which prompted months of escalated military tensions that saw Pyongyang issue apocalyptic threats of nuclear war against Seoul and Washington.