The ceasefire started at 7:00 a.m. (0500 BST) to allow for negotiations over the fate of nine Lebanese soldiers who have been in Islamic State captivity since 2014, the army said.
Lebanese militant group Hezbollah launched its own simultaneous attack against IS from the Syrian side of the border in an area known as west Qalamun.
"In reality, the Syrian army and its allies have formed a circle, surrounding the Daesh militants on a vast territory of some 2,000 square kilometers [approximately 772 square miles]", the source said.
The militants have been fighting the Lebanese army on one front, and Hezbollah with the Syrian army on the other.
Any coordination between the Lebanese army and either the Syrian army or Hezbollah would be politically sensitive in Lebanon and could jeopardise the sizeable US military aid the country receives.
ISIS was permitted to withdraw to Deir al-Zor province, which borders Iraq to the east and is nearly entirely under Islamic State control. Sixteen were released in a prisoner swap in December 2015.
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The next day, during a news conference in NY , he reverted to his original stance, declaring that "there's blame on both sides ". But Trump, in his retelling of his initial statement, omitted the line " on many sides " that had drawn so much criticism.
Lebanon has said the nine troops taken hostage by IS are its "top concern" in the offensive against an estimated 600 IS fighters.
"The negotiations are ongoing for IS to withdraw and provide information on the fate of the troops".
The photo shows Lebanese army soldiers in the town of Ras Baalbek on August 21, 2017.
Earlier this week, the army and its allies encircled the IS militants after advancing southward to join up with their forces near al-Sukhna town in Homs province.
Al-Nusra and IS each executed two of their hostages, and a fifth died of wounds sustained during the fighting in Arsal.