Suleiman made the remarks while meeting with the Lebanese community in the Ivory Coast during an official visit, according to a statement from his office on Saturday.
Lebanon’s stability depends “on all of us… not sending militants to Syria and not receiving them,” he said, adding “we must commit ourselves to neutrality.”
Suleiman said he had tasked Lebanon’s army with “the arrest of any militants intending to fight (in Syria), whether for the opposition or not.”
His comments came after Syria warned on Thursday that its forces would fire into Lebanon if “terrorist gangs” continued to infiltrate the country.
“These past 36 hours, armed terrorist gangs have infiltrated Syrian territory in large numbers from Lebanon,” the Syrian foreign ministry said, in a message quoted by official news agency SANA.
“Syrian forces are showing restraint by not striking these gangs inside Lebanese territory to prevent them crossing into Syria, but this will not go on indefinitely,” it said in a message to its Lebanese counterpart.
A Lebanese government source, speaking to AFP on Saturday, said Beirut took the warning “very seriously” and that “intensive consultations are underway to find the best way to control the border.”
Lebanon’s opposition March 14th movement, which opposes the Damascus regime, has called for the army to deploy along the country’s border with Syria to halt the flow of arms and militants, and protect Lebanese territory.
Beirut has officially pledged neutrality in the violence engulfing its neighbor, but has found itself increasingly embroiled in the civil war.
Lebanon’s opposition backs the revolt, which entered its third year on Friday, while the Shiite Hezbollah and its allies stand by the regime.
Violence has already spilled over into Lebanon on several occasions, causing fatalities on the Lebanese side, and on Thursday the UN Security Council expressed “grave concern” about cross-border attacks.