"We have no meetings or no plans and no travel to announce at this point", Nauert said. No specific date has been set.
He said he hoped for speedy progress in talks between the United States and North Korea, with steps by Pyongyang to abandon its nuclear programmes matched by "corresponding comprehensive measures" from Washington.
But he added that any improvement of inter-Korean ties was not dependent on relations between Pyongyang and Washington.
"North Korea-US summit too has been successfully held on the strong determination of the North and the US to move toward peace and prosperity", the president said referring to the historic summit between US President Donald Trump and the North Korean leader held in Singapore on June 12.
Moon and Kim committed during their first meeting in April to connecting their road and rail networks as a "first step" toward restarting economic cooperation.
A group of war veterans from the former Soviet Union participated, and thousands of people cheered their soccer team to victory over a South Korean squad in the opening match of an under-15 youth tournament in Pyongyang featuring players from several countries. No sitting South Korean leader has attended the North Korean anniversary events.
Moon has championed efforts to bring peace to the Korean Peninsula since taking office previous year, and played a crucial role in bringing Kim and U.S. President Donald Trump together for their historic first summit in June.
Once peace is established, Moon said that other economic projects would be pursued, including the creation of special economic zones in South Korean provinces that border the North. Pyongyang has been calling for an end-of-war declaration as a security guarantee in return for taking denuclearization actions.
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That's crucial to Kim, who is hoping to undermine support for the US -backed sanctions so that he can focus on improving North Korea's economy.
The US has urged the worldwide community to maintain tough sanctions on the isolated regime.
To lift economic sanctions, the United States insists the North take tangible denuclearization steps such as submitting a listing of its nuclear arsenal and nuclear and missile facilities. He also said work would begin this year.
Cho said he also urged the North Koreans to accelerate the nuclear negotiations with the U.S. The North said it was making efforts to disarm, but Cho said there were no new details on those efforts.
"In a realistic sense, this is the major transformation in the inter-Korean relationship", Ri said.
During an address Wednesday, South Korean leader Moon Jae-in expressed optimism and willingness to sign a peace treaty to officially bring an end to the Korean War. Such as announcement could take place at the United Nations General Assembly meeting in New York City.