Adnan Mansour said he had been in touch with a number of Arab officials and his Turkish counterpart to try to secure the captives' return to Lebanon.
“They will be released in the coming hours,” Mansour said, according to Lebanon's state news agency. The report gave no further information on the captives' location or on who is holding them.
The kidnappings come at a time of deep tension in Lebanon over Syria. News of the abduction on Tuesday night set off protests in Beirut's southern suburbs, a Shiite area, where residents burned tires and blocked roads.
Syria's state news agency blamed rebels for the kidnapping. It said the Lebanese group was on its way home from a religious pilgrimage in Iran when rebels intercepted their vehicles and abducted the 11 men and their Syrian driver. Lebanese security officials confirmed the kidnapping.
The protests in Beirut quieted down when the leader of Hezbollah, the Lebanese Shiite militant group, urged calm in a TV address.
“This is strictly prohibited,” Sheik Hassan Nasrallah said of the protests. “We will work day and night until these beloved people are with us.”
Syria's uprising began in March 2011 with mostly peaceful calls for reform, but the government's brutal crackdown on dissent led many in the opposition to take up arms. The UN estimates more than 9,000 people have been killed as the conflict spirals toward civil war.
Lebanon and Syria share a complex web of political and sectarian ties and rivalries, which can quickly turn violent.
Earlier this month, the arrest of an outspoken Lebanese critic of Syrian led to gunbattles in the northern city of Tripoli that killed at least 8 people and injured many more.
World powers have pinned their hopes on a peace plan to end Syria's conflict brokered by international envoy Kofi Annan that calls for a cease-fire by all sides to allow for dialogue on a political solution.
But that plan is under strain. A cease-fire between government troops and rebels that was supposed to start last month has never really taken hold.
And the prospects for talks between the regime and those seeking to topple it appear as distant as every. President Bashar Assad's government has never acknowledged popular calls for reform in the country and dismisses the opposition as “armed terrorists.”
For their part, opposition leader say the regime has killed too many civilians to play a role in the conflict's solution.
Late Tuesday, a UN team in Syria meant to monitor the cease-fire said it had brokered an exchange between forces loyal to Assad and opposition fighters seeking to topple his regime.
A UN statement said government forces released two detainees from the town of Khan Sheikhoun in northwest Syria in exchange for permission to retrieve a destroyed tank.