Bassil "met ambassadors from the powerful five permanent members of the UN Security Council today (Friday) and discussed with them the establishment of camps for Syrian refugees along the border," a ministry statement said.
Those talks were followed by a meeting with Syrian Ambassador Ali Abdel Karim Ali to discuss the question of refugees, who now number more than a million in Lebanon.
Afterwards, Damascus's envoy told reporters that his country opposed the idea.
"We are against such camps... Syria is a large country that can accommodate all of its citizens," he insisted.
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Lebanon is the only country bordering Syria to practise an open border policy, but highlights the economic burden of the Syrian refugee presence.
More than three years of conflict have created millions of refugees in addition to more than 162,000 dead,
Refugees now account for a quarter of the population of Lebanon and cost Beirut $4.5 billion (3.3 billion euros) a year, according to Central Bank Governor Riad Salameh.
In May, the International Monetary Fund estimated that because of the conflict in neighbouring Syria, unemployment in Lebanon had nearly doubled.
It said the number of people without jobs had hit about 20 percent, and noted that growth of 2 percent was well below pre-Syria crisis levels.