North and South Korea are likely to be a focal point of the Games, particularly amid recent doubts over Kim's promise to work towards denuclearisation made during a summit with U.S. President Donald Trump in Singapore in June.
Ministers from the two Koreas agreed in April to push for a unified delegation from both countries to parade together in the opening ceremony at the Asian Games, to be staged in August and September.
Indonesian officials led by Coordinating Human Development and Cultural Affairs Minister Puan Maharani visited North Korea this week, meeting with Kim Yong Nam, the nominal head of state and president of the Presidium of the Supreme People's Assembly.
"The main reason for us coming (to Pyongyang) is to convey an official invitation to the President of North Korea to attend the Asian Games Opening Ceremony on August 18," Maharani said in a release issued by the National Police.
Maharani also discussed North and South Korea relations during the visit, as well as regional issues and the performance of Indonesia's police in countering militancy.
The Pyongyang visit follows the delivery of a similar invitation in Seoul last week.
President Moon "will consider attending, with circumstances such as future schedule in mind," Blue House Spokesman Kim Eui-kyeom said in an emailed statement.
Widodo offered in April to host a summit between North and South Korea, after meeting ambassadors from both Koreas.
The two countries marched under a unified flag at the opening and closing ceremonies of February's Winter Olympics in Pyeongchang. The Asian Games, co-hosted by the cities of Jakarta and Palembang, are expected to see a further cementing of that partnership.
Deputy National Police chief Syafruddin, among the Indonesian delegation in Pyongyang, said Indonesia guaranteed security to all countries and contingents present at the Asian Games, including the government of North Korea.
"Indonesia's security is very stable. Don't worry or hesitate," said Syafruddin, who like many Indonesians goes by only one name.
(Reporting by Jessica Damiana in JAKARTA; additional reporting by So Young Kim in SEOUL; writing by Fergus Jensen; editing by Paul Tait and Richard Pullin)
