"In the charter of SCO, there is a clause that hostility in the bilateral relations should not be brought to the organisation," Kong said.
"I believe those countries will abide by the charter of this organisation."
"This organisation has its own rules and procedures. We hope that these rules are abided by all member states," Kong added.
He was talking to Indian journalists on the sidelines of an SCO event where national flags of India and Pakistan were hoisted after the two countries were admitted to the group last week in Astana, Kazakhstan.
China is worried that bilateral disputes between India and Pakistan could affect the forum.
However, a senior Pakistani diplomat earlier said the SCO was not a forum to settle bilateral disputes.
The envoys of India and Pakistan Vijay Gokhale and Masood Khalid respectively were present on the occasion at the SCO Secretariat.
Addressing the event, Gokhale said: "Now as a full member of SCO, we look forward to further deepening these relations for mutual benefit."
"We would also like to deepen our cooperation in our joint fight against terrorism."