Controversy over Hezbollah's weapons intensified after its fighters captured two Israeli soldiers in a cross-border raid in 2006, sparking a 34-day war that left more than 1,000 Lebanese dead and the infrastructure of southern Lebanon devastated.
Having gained political clout after that conflict, Hezbollah supporters and other opposition groups camped outside parliament, demanding greater legislative representation.
Tensions then boiled over further last May, when opposition fighters took control of west Beirut in unrest that left 65 people dead - the worst internal conflict since the 1975-1990 civil war.
The violence led to talks in Doha, the Qatari capital, and an agreement that stipulated the election of Sleiman, formation of a new government, agreement on a law for next year's parliamentary election and the holding of talks to discuss divisive issues.
Sleiman's comments on the latest talks came at an iftar - a fast-breaking dinner - held for Lebanese leaders to mark Ramadan, a holy month for Muslims.
"We are not against any meeting particularly one with Sayyid Nasrallah. We are for the meeting, but in its time"
Saad al-Hariri, Lebanese parliamentary majority leader
Shortly before, Saad al-Hariri, the parliamentary majority leader and son of an assassinated former prime minister, said he was open to a proposal by Hassan Nasrallah, the leader of Hezbollah, for direct talks.
"The doors of Qoraytem [al-Hariri's residence] are not closed to anyone," he said.
"We are not against any meeting particularly one with Sayyid [Hassan] Nasrallah. We are for the meeting, but in its time."
In comments published by Lebanese newspapers on Monday, Nasrallah had urged al-Hariri to meet him for reconciliation talks.
"I have said that I am ready to sit down with him - there's no disagreement about the principle of a meeting, only about the venue," Nasrallah said.
"Our head-to-head has not taken place because of the security concerns facing both him and me."
Sleiman's announcement also came a day after rivals in Tripoli, northern Lebanon's main city, signed a reconciliation agreement aimed at restoring state control to the port and ending violence there.
At least 23 people were killed in Tripoli during clashes in May between residents of Jabal Mohsen, who mostly support the Hezbollah-led opposition, and those in Bab al-Tebbaneh who back the anti-Syrian ruling bloc.