Kim delivered a similar message to Chinese President Xi Jinping in a reply published by KCNA on Sunday.
The three countries, however, have stressed that the agreement is defensive and not aimed at any particular state.
“The practical work on this agreement will begin in the coming days, and discussions will focus on how to implement it effectively,” he said.
The deal is expected to strengthen defense and security cooperation between the two countries.
The meeting focused on the current situation and prospects for expanding cooperation in areas of mutual interest between the two sides.
The mutual defence deal was signed following Israel's strikes on what it said were Hamas targets in Doha, an attack that shook the Gulf region.
The senior Saudi official, who spoke on condition of anonymity, acknowledged the need to balance relations with Pakistan's rival, India, also a nuclear power.