Kim made the remark during a meeting with lawmakers of the parliamentary committee for unification and foreign affairs, according to local media reports.
According to the minister, ROK will seek first to repair its own section of the cross-border railways and roads while continuing efforts to re-link and modernize railways and roads along the eastern and western Korean Peninsula.
The two Koreas held a groundbreaking ceremony in December 2018 at the DPRK's border town of Kaesong for the reconnection project, but construction works had yet to start owing to international sanctions against Pyongyang.
In his New Year speech last month, ROK President Moon Jae-in offered a broader inter-Korean cooperation this year to the DPRK.
The reconnection project was agreed upon by Moon and the Chairman of DPRK Kim Jong Un following their first summit in April 2018. The two Koreas had jointly conducted on-spot surveys on the eastern and western railways and roads of the DPRK.
The ROK minister said the government will also push for ROK people individual tour to the DPRK, while seeking to co-host the 2032 Summer Olympics together with the DPRK.
The two Koreas already delivered their intent to jointly play host to the 2032 Olympics to the International Olympic Committee.