Lebanese lawmakers are divided over an armed Hezbollah, a member of the Lebanese government designated by the United States as a terrorist organization.
Some lawmakers say an armed Hezbollah is needed to deter Israeli aggression, though opponents claim that's what giving Israel an excuse to maintain a defensive posture.
Suleiman said he would continue seeking a resolution in the spirit of national security.
"I underscore my intention to continue efforts to provide the necessary conditions for the resumption of dialogue between the various parties in order to protect the Lebanese and to make every effort to agree on a defense strategy for Lebanon," he was quoted by Lebanese newspaper The Daily Star as saying.
Hezbollah is obligated under a U.N. mandate to disarm.
A Lebanese national was arrested Friday in Thailand on suspicion of plotting attacks on sites in Bangkok popular with Western tourists. The Thai government said it believed the suspect was a member of Hezbollah, CNN International reports. Hezbollah denied the charges.