(CNN) Secretary of Defense James Mattis says "there's no wedge" between the United States and South Korea, despite recent overtures between South Korea and North Korea.

"I know that people are watching for a wedge between South Korea, Republic of Korea, in other words and the United States," Mattis told reporters on a flight to Rome. "There's no wedge there, the military staffs are integrated. If you move up to the political level, Admiral Song, minister of defense Song, flew into Hawaii when I was out in the Pacific, that's so he and I could sit down face to face and consult."

Mattis' remarks come after South Korean President Moon Jae-in was presented a formal invitation to visit North Korea, potentially setting up the first meeting of Korean leaders since 2007.

The invitation was made by Kim Yo Jong, the younger sister of North Korean leader Kim Jong Un, during a historic meeting between North and South Korean officials at Seoul's presidential palace Saturday, presidential spokesman Kim Eui-kyeom said.

Moon responded to the invitation by suggesting the two countries "should accomplish this by creating the right conditions," adding that talks between North Korea and the United States were also needed, and requested that North Korea be more active in talking with the US, according to the spokesman.

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