In this June 12, 2018, file photo, U.S. President Donald Trump, right, meets with North Korean leader Kim Jong Un on Sentosa Island, in Singapore. AP

The United States reaffirmed Monday that inter-Korean cooperation should proceed "in lockstep" with progress in North Korea's denuclearization, as Seoul continued to push for individual tours to the North.

Earlier, Seoul's unification ministry said it is looking at ways to hold talks with Pyongyang on allowing tours to North Korea on an individual basis. The push has gained traction after President Moon Jae-in cited it last week as a way to expand inter-Korean exchanges without violating sanctions.

"The United States supports inter-Korean cooperation and coordinates with our ROK ally to ensure inter-Korean cooperation proceeds in lockstep with progress on denuclearization," a State Department spokesperson told Yonhap News Agency, using the abbreviation for South Korea's official name, the Republic of Korea.