Talks between the two countries about participation in the September showpiece in Incheon ended last week with the North threatening to pull out of the Games.
They were unhappy that their larger-than-expected party of 350 athletes and a similar amount of cheerleaders was not agreed to by the South.
The North's KCNA official news agency ran a statement from the Committee for the Peaceful Reunification of the Fatherland on Wednesday pushing the South to accept the deal.
"No one should have impure intent to misuse pure sports activity for political purposes," it said.
"The South Korean authorities should not lose this golden opportunity for improving North-South relations."
North Korea, subject to U.N. sanctions for its missile and nuclear programmes, routinely threatens to destroy its neighbour and have test fired several short-range missiles and rockets over the past few months.
Its leaders demand the South halt routine joint military drills with the United States. South Korea has urged the North to take steps to end its nuclear programme.
The North, who have threatened to conduct a fourth nuclear test, have recently proposed steps to ease tension and believed participation in the Games would also help.
"Our national teams and cheerleading squad decided to participate in the 17th Asian Games because, although the geopolitical tension is high, we wanted to build up the festive atmosphere for the feast hosted by the same people, improve the inter-Korean relations and dissipate mutual distrust."
Last week's meeting was also meant to discuss transportation and accommodation for the North's contingent, including the ever popular cheerleaders.
Their tightly choreographed gymnastic routines and messages of peace and unification have proved a huge attraction in rare appearances in the South since the end of the 1950-1953 war.
In 2005, Pyongyang sent 101 cheerleaders, including Ri Sol Ju, who has since married North Korean leader Kim Jong Un, to the Asian Athletics Championships in Incheon.
To help lessen the burden on the South, the North said they were willing to house all their entourage on a ship at the port city for the duration of the Sept. 19 to Oct. 4 Games.
They were upset their offer wasn't accepted and said if the South "wants to waste time arguing over these problems without understanding our generosity and efforts, this is just a shame that invites only criticisms and humiliation."
"If our teams and cheerleading squads do not participate in the Games that take place in Incheon, very close to the demarcation line, it will only be a great humiliation to our people and descendents," the statement added.
"We will act with patience in discussing the participation in the Games in a way that we can proactively contribute to the rapport and peace of many countries not only in Asia but in the world."
(Writing by Patrick Johnston; editing by Amlan Chakraborty)
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