Israeli allegations last month that Syria had transferred long-range scud missiles to Hezbollah fueled security concerns although Lebanon and Syria both denied the charge, while Hezbollah leader Sayyed Hassan Nasrallah has refused to comment.
Hezbollah is on the United States' terrorism blacklist but it is also part of the Lebanese government.
Syria says it only gives Hezbollah political backing and that Israel may be using the accusation as a pretext for a military strike.
Hezbollah and Israel fought a 34-day war in the summer of 2006 during which the powerful resistance group fired thousands of mostly short-range rockets against the Zionist state.
"To demand now, in this regional atmosphere full of dangers and the drumbeats of war that Israel is banging everyday, and before we reach an agreement on a national defense strategy to protect Lebanon, we cannot and must not tell the resistance ... 'Give us your weapons and put it under the state's command'," Suleiman was quoted as saying in Ad-Diyar newspaper on Saturday.
The current government, led by Sunni Muslim businessman Saad Al-Hariri, has backed Hezbollah's right to keep its weapons to deter Israeli attacks, an issue that has been at the heart of Lebanon's political crisis over the past five years.
Suleiman has chaired periodic "national dialogue" sessions but politicians have been unable to agree on a national defense strategy, in which Hezbollah's weapons would be integrated into thearmy, to protect Lebanon from Israel.
Israel is worried the Iranian-backed group has replenished its arsenal to attack it on Iran's behalf should Tehran's nuclear sites come under attack.
Security Council resolution 1701, which halted hostilities between the Israeli-Hezbollah war in 2006, calls for a stop to arms smuggling. It bans all unauthorized weapons between the Litani River and the Blue Line, the UN-monitored border between Israel and Lebanon.
Israel has criticized the UN peacekeeping force in southern Lebanon, UNIFIL, for not stopping weapons it says are flowing to Hezbollah fighters. The United Nations says that is the responsibility of the Lebanese authorities.
UN Security Council Resolution 1559, sponsored by the United States and France and adopted in 2004, demanded that all Lebanese militias be disarmed. Hezbollah is the only group to have kept its arms since the 1975-1990 civil war.
