The meeting comes a day after the North's delegation, including leader Kim Jong Un's younger sister Kim Yo-jong, met South Korean President Moon Jae-in.
Moon suggested the two Koreas "make it happen" by creating conditions necessary for him to accept the invitation, the spokesman told a news briefing.
And Kim's sister, Kim Yo-jong, made history by becoming the first member of the North's ruling family to visit the South since the Korean War in the mid-20th century.
However, North Korean athletes are taking part in the Olympics, with the two countries agreeing to field a unified ice hockey team.
"The inter-Korean relations should be mended by the parties concerned at any cost", Moon was quoted by the agency as adding.
Experts say that it is critical for South Korea to get the US and other partners on board in its efforts to turn the current peace mood being created by the Olympics - and the North's participation therein - into meaningful steps to denuclearize the North, a task the foreign ministry is supposed to spearhead going forward.
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Such a meeting, if it came about, would mark the first inter-Korea summit since 2007. Pence endorsed a change of tactics after Moon assured him the North Koreans wouldn't get economic or diplomatic benefits just for talking - they must take concrete steps toward denuclearization.
Loud applause greeted the appearance of Moon, Kim Yo Jong and her delegation at the concert, attended by more than a thousand people. The White House official said the invitation didn't undermine or detract from Pence's trip.
"(The visit) shows North Korea's will to improve inter-Korean ties is very strong and if needed it will take unprecedented and aggressive measures", the ministry said. "But if you want to talk, we'll talk".
Kim Yo-jong carried a bright blue folder as she entered the conference room at the Blue House, Seoul's presidential office, and some analysts speculated it could contain a letter from her brother.
Major protests have erupted in South Korea as activists burn the North's flag.
"What can not be overlooked is that Moon did not directly demand North Korea to abandon its nuclear development".