The UN Security Council is gravely concerned over the incident concerning the sinking of the Republic of Korea (ROK)'s naval warship Cheonan, the council president said Monday.

The Security Council "is gravely concerned with this incident that caused the deaths of 46 sailors and its impact on peace and stability on Korean Peninsula," Mexico's UN Ambassador Claude Heller, the council president for this month, told reporters.

"The Security Council makes strong call to the parties to refrain from any act that could escalate tensions in the region and makes an appeal to preserve peace and stability in the Korean Peninsula," he said.

The president made the remarks after the 15-nation council held two separate meetings with the Republic of Korea (ROK) and the Democratic People's Republic of Korea (DPRK) to discuss ROK's warship sinking case.

The closed door meetings, which lasted nearly four hours, were conducted in the format of "private interactive dialogue," which meant only to provide an opportunity for council members to listen to briefings from the concerned parties.

Representatives from the ROK delegation, which was composed of diplomats, military officers, experts and foreign observers, made a presentation to and answered questions from the council members, UN diplomats close to the meeting said.

When meeting with the council, the DPRK side repeated a request to send its own inspectors to the ROK to verify the so-called evidence related to the incident, the diplomats said.

The council did not reach any conclusion yet and will "continue its consultations on this incident," Heller said.

On June 4, ROK send a letter to Heller, formally requesting the Security Council to take action over the case of "Cheonan" "in a manner appropriate to the gravity of situation."

Seoul said after completing investigations that the warship was torpedoed by the DPRK. But Pyongyang denied its involvement in the incident.