The demand, among a set of proposals made by North Korea's powerful National Defence Commission, showed that the North intends to use its participation in the games as a negotiating card with South Korea, analysts say.
The Asian Games are scheduled to take place in the South Korean city of Incheon from September 19 to October 4.
Analysts say North Korea is pursuing better ties with the outside world to obtain investment and aid to revive its troubled economy.
Today, the North's defense commission said it wants South Korea-US military drills planned for August to be scrapped immediately, saying they are a preparation for an attack.
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It didn't say what it would do if the drills go ahead. The allies have said they have no intention of invading the North.
"With its Asian Games participation as a negotiation tool, North Korea is pushing for South Korea to cancel the drills or conduct them in a dramatically less threatening manner," said Lim Eul Chul, a North Korea expert at South Korea's Kyungnam University.
North Korea boycotted the 1986 Asian Games and the 1988 Summer Olympics, both in Seoul, but attended the 2002 Asian Games in Busan and the 2003 University Games in Daegu.
The defence commission, in a statement carried by state media, proposed that the two Koreas halt hostile military acts against each other at border areas and stop psychological warfare starting Friday, the 42nd anniversary of a historic 1972 joint statement on peaceful reunification.
The proposals are largely seen as testing whether the conservative South Korean government of President Park Geun-hye, who faces public criticism following a deadly ferry disaster in April, wants to break the deadlock in inter-Korean ties, Lim said.